Differential Equations — practice questions

144 curated practice questions from Differential Equations (Mathematics JEE Main, NTA Exams) — 102 easy, 20 medium, 22 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.

• The solution of the equation (y-x d y d x ) ( d y d x -1 )= d y d x is,
• The solution of the differential equation (1+y^ 2 )+ (x-e^ ^ -1 y ) d y d x =0 is
• The solution of the differential equation x d y d x =y-x ( y x ) is ,
• The order of the differential equation whose general solution is given by y= (C_ 1 +C_ 2 ) (x+C_ 3 )-C_ 4 e^ x+C_ 5 …
• Let y = y(x) be the solution of the differential equation x d y d x +y x=4 x, x (0, ) . If y ( 2 )=0 , then y ( 6 ) is…
• The degree of the differential equation ( d^ 2 y d x^ 2 )^ 2 + ( d y d x )^ 2 =x ( d^ 2 y d x^ 2 ) is
• The curve passing through the point (0, 1) and satisfying the equation sin ( dy dx ) = a is :
• The solution of the equation d y d x = (1+x) y (y-1) x is :
• The solution of the differential equation (4 x+2 y-2) d x-(2 x+y+1) d y=0 :
• If y=y(x) is the solution of the differential equation d y d x =( x-y) ^ 2 x, x (- 2 , 2 ) , such that y(0)=0 , then y…
• Let y = y(x) be the solution of the differential equation, d y d x +y x=2 x+x^ 2 x, x (- 2 , 2 ) , such that y(0)=1 …
• The solution of e^ d y d x =(x+1) where y(0)=3 , is
• Equation of curve through point (1, 0) which satisfies the differential equation (1 + y 2 ) dx – xy dy = 0, is
• The solution of the differential equation d y d x = x+y x satisfying the condition y(1)=1 , is
• The solution of the differential equation (x+y)^ 2 d y d x =a^ 2 is,
• Let the population of rabbits surviving at a time t be governed by the differential equation d p(t) d t = 1 2 p(t)-200…
• The solution of the equation d^ 2 y d x^ 2 =e^ -2 x is,
• The solution of dy dx = 1 +x + y + xy is
• Water is dropped at the rate of 2 m 3 /sec into a cone of semi vertical angle of 45°. The rate at which periphery of…
• The equation of a curve passing through (2, 7 2 ) and having gradient 1- 1 x^ 2 at (x, y) is
• The solution of the differential equation d y d x + 1+x^ 2 x =0 is
• The order and degree of the differential equation (1+3 d y d x )^ 2 3 =4 d^ 3 y d x^ 3 is,
• If d y d x =y+3>0 and y(0)=2 , then y( 2) is equal to
• The degree and order of the differential equation of the family of all parabolas whose axis is x -axis, are respectively
• The general solution of the differential equation (e^ x +e^ -x ) d y d x = (e^ x -e^ -x ) is
• The solution of the equation x^ 3 d y d x +4 x^ 2 tan y = e x sec y satisfying y (1) = 0, is
• The solution of y_ 1 -8 y_ 2 =0 satisfying y (0)= 1 8 , y _ 1 (0)=0 and Y _ 2 (0)=1 is :
• The equation of the curve for which the tangent at P (x, y) cuts the y – axis at (0, y 3 ) is
• The solution of the differential equation y_ 1 +3 x y=x which passes through (0,4) is,
• The equation of the curve in which subnormal varies as the square of the ordinate is (λ is constant of proportionality)
• Let the population of rabbits surviving at a time t be governed by the differential equation d p(t) d t = 1 2 p(t) –…
• The solution of the differential equation d y d x +2 y x= x, y ( 3 )=z :
• The solution of the differential equation x d y d x +2 y=x^ 2 (x 0) with y(1)=1 , is
• The integrating factor of the differentiable equation (xy – 1) dy dx + y ^ 2 =0 is
• The solution of differential equation x 2 y dx – (x 3 + y 3 ) dy = 0 is
• The solution of differential equation 2 x^ 3 y d y+ [1-y^ 2 ) [x^ 2 y^ 2 +y^ 2 -1 ] d x=0
• The solution of the differential equation (e^ -2 x - y x ) d x d y =1 is given by
• The solution of the differential equation d y d x =(3 x+y-1)^ 2 is,
• If x d y d x -y x=6 x, (0<x< 2 ) and v ( 3 )=0 , then y ( 6 ) is equal to:
• The solution of differential equation (x 2 –1) dy dx + 2 xy = 1 x^ 2 -1 is
• The solution of differential equation (x^ 2 -y x^ 2 ) d y+ [y^ 2 +x^ 2 y^ 2 ) d x=0 is,
• The solution of differential equation d y d x +y= 1+ x 1+ x , is
• Consider the differential equation y^ 2 d x+ (x- 1 y ) d y=0 . If y (1) = 1, then x is given by
• The solution of the differential equation x d x+y d y x d y-y d x = 1- (x^ 2 +y^ 2 ) x^ 2 +y^ 2 is,
• The solution of (x 1+ y ^ 2 )dx + (y 1+x^ 2 )dy = 0 is -
• STATEMENT - 1 (Assertion): y=a x+b x is a general solution of y^ +y=0 . STATEMENT - 2 (Reason): y=a x+b x is a…
• If y=y(x) satisfies the differential equation (2+ x) d y d x +(1+y) x=0, y(0)=1 then y ( 2 ) is equal to
• The solution of the differential equation cos y log (sec x + tan x) dx = cos x log (sec y + tan y ) dy is
• Solve the differential equation (x^ 2 ^ 3 y-y^ 2 x ) d x+ (x^ 3 y ^ 2 y-2 y x ) d y=0 .
• The solution of the differential equation d y d x = ^ 2 (x+y) is,
• Let y=y(x) be the solution of the differential equation, (x^ 2 +1 )^ 2 d y d x +2 x (x^ 2 +1 ) y=1 such that y(0)=0 …
• The degree of the differential equation [1+ ( d y d x )^ 2 ]^ 5 3 = d^ 2 y d x^ 2 is :
• The general solution of the differential equation [2 x y -x] dy + y dx = 0 is
• The general solution of the differential equation y(x 2 y + e x ) dx – e x dy = 0 is
• The general solution of y^ 2 d x+ (x^ 2 -x y+y^ 2 ) d y=0 is,
• Solution of the differential equation cos x dy = y (sin x – y) dx, 0 < x < 2 , is
• If y(t) is a solution of the differential equation (1+t) d y d t -t y=1 and y(0)=-1 , then y(1) is equal to
• The solution of the differential equation d y d x = x+y x satisfying the condition y (1) = 1 is
• The solution of differential equation dy dx – y tan x = – y 2 sec x is :
• To reduce the differential equation d y d x +P(x) y=Q(x) y^ n to the linear form, the substitution will be
• The differential equation of all non-vertical lines in a plane is
• The solution of the differential equation (x+2 y^ 3 ) d y d x =y y(z)=1 is,
• The solution of the differential equation (x x) d y d x +y=2 x , is
• STATEMENT - 1 (Assertion): The degree of the differential equation d^ 2 y d x^ 2 + d y d x = ( d^ 2 y d x^ 2 ) is 2…
• If φ (x) is a differentiable function, then the solution of the differential equation d y+ y ^ (x)- (x) ^ (x) dx = 0 is
• The solution of Differential equation d y d x = x+2 y-3 2 x+y-3 is
• The differential equation of all circles passing through the origin and having their centres on the x-axis is
• STATEMENT - 1: The order of the differential equation whose general solution is y=c_ 1 2 x+c_ 2 ^ 2 x+c_ 3 ^ 2 x+c_ 4…
• An integrating factor of the differential equation x d y d x +y x=x e^ x x^ - 1 2 x , (x > 0) is,
• The solution of the differential equation 1+x^ 2 +y^ 2 +x^ 2 y^ 2 +x y d y d x =0 is,
• The solution of the equation x^ 2 d^ 2 y d x^ 2 = x when x =1_ 1 y = 0 and d y d x =-1 is,
• STATEMENT - 1 (Assertion): The differential equation of all circles in a plane must be of order 3. STATEMENT - 2…
• The solution of the differential equation d y d x = 3 x^ 2 y^ 4 +2 x y x^ 2 -2 x^ 3 y^ 3 is,
• The solution of the differential equation d y d x = 2+x-y 3+2 x-2 y is,
• The solution of the differential equation [y (1+x^ -1 )+ y ] d x+(x+ x+x y) d y=0 is,
• Solution of the differential equation x d y=y( x-y) d x (0 , is
• The general solution of the differential equation (1 + y 2 ) dx + (1 + x 2 ) dy = 0 is
• The general solution of the differential equation, 2 x ( d y d x - x )-y=0, is:
• The solution of differential equation d y d x +y x=2 x+x^ 2 x, y(0)=0 is,
• STATEMENT - 1 (Assertion): The elimination of four arbitrary constants in y= (c_ 1 +c_ 2 +c_ 3 e^ I_ 4 ) x results into…
• If y^ -3 y^ +2 y=0 where y(0)=1, y^ (0)=0 , then the value of Y at x= 2 is :
• Let y = y(x) be the solution of the differential equation, x d y d x +y=x _ e x,(x>1) . If 2 y(2)= _ e 4-1 , then y(e)…
• The solution of the differential equation d y d x - y+3 x _ e (y+3 x) +3=0 is: (where C is a constant of integration)
• The solution of the differential equation y_ 1 1+x+y =x+y-1 is ,
• Let y = y(x) be the solution curve of the differential equation (y^ 2 -x ) d y d x =1 , satisfying y(0) = 1. This curve…
• Solve ( d y d x ) y= (x+y)+ (x-y) .
• The general solution of the differential equation y d x+ (1+x^ 2 ) ^ -1 x d y=0 is,
• The solution of the differential equation (1+y^ 2 ) d x= [ ^ -1 y-x ] d y is :
• The solution of (cosec x log y)dy + (x 2 y)dx=0 is -
• If x d y d x =y (log y – log x + 1), then the solution of the equation is
• The solution of the differential equation (1+e^ x y ) d x+e^ x y (1- x y ) d y=0 is :
• If y(x) is the solution of the differential equation d y d x + ( 2 x+1 x ) y=e^ -2 x , x>0 , where y(1)= 1 2 e^ -2 …
• The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point…
• Form the differential equation representing the family of curves y = A cos 2x + B sin 2x, where A and B are constants.
• The solution of the differential equation d y d x = y ^ (x)-y^ 2 (x) where ( x ) is a specified function is :
• Consider the differential equation, y^ 2 d x+ (x- 1 y ) d y=0 , If value of y is 1 when x = 1, then the value of x for…
• The solution of the differential equation, d y d x =(x-y)^ 2 , where y(1)=1 , is:
• The solution of differential equation ( d y d x )=a x+b y is,
• The solution of the differential equation d y d x =1+x+y+x y is,
• The solution of y=x ( d y d x + ( d y d x )^ 3 ) , where p= d y d x is given by
• The solution of the differential equation d y d x = y+x 2 y-x y is
• The differential equation d y d x = 1-y^ 2 y determines a family of circles with
• The solution of d y d x = e^ x ( ^ 2 x+ 2 x ) y(2 y+1) is-
• Solution of the differential equation d y d x +a y=e^ m x is,
• The curve amongst the family of curves represented by the differential equation, (x^ 2 -y^ 2 ) d x+2 x y d y=0 which…
• A curve passes through the point (0, 1) and the gradient at (x, y) on it is y (xy – 1). The equation of the curve is
• The solution of the differential equation d y d x + 2 y x 1+x^ 2 = 1 (1+x^ 2 )^ 2 is,
• The solution of differential equation d y d x = (x+y)+ (x+y) is,
• The solution of the differential equation x x^ 2 +y^ 2 d y= ( y x^ 2 +y^ 2 -1 ) dx is
• The curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact…
• The solution of the differential equation y d x+ [x+x^ 2 y ] d y=0 is,
• If f^ (x)=f(x)+ _ 0 ^ 2 f(t) d t, f(0)= 4-e^ 2 3 , then function f(x) is
• The solution of differential equation dy dx = sec (x + y) is
• If sin x is an integrating factor of the differential equation dy dx + Py = Q, then P can be
• The general solution of the differential equation 2 x d y d x -y=3 is a family of :
• The solution of the differential equation d y d x =y x-2 x_ 1
• STATEMENT - 1 (Assertion): The differential equation of the form y f(x y) d x+x (x y) d y=0 can be converted to…
• Determine the equation of the curve passing through the origin which satisfies the differential equation, d y d x = (10…
• Which of the following differential equations has the same order and degree-
• The solution of the differential equation e^ -x (y+1) d y+ [ ^ 2 x- 2 x ] y d y=0 is,
• The solution of the differential equation xy d y d x = (1+y^ 2 ) (1+x+x^ 2 ) (1+x^ 2 ) is -
• The differential equation which represents the family of curves y = c _ 1 e ^ c _ 2 x where c 1 and c 2 are arbitrary…
• Solve x x ( d y d x )+y(-x x+ x)=1 .
• The degree of the differential equation corresponding to the family of curves y = a (x + a) 2 , where a is an arbitrary…
• STATEMENT - 1 (Assertion): Order of the differential equation whose solution is y=c_ 1 e^ x+i_ 2 +c_ 3 e^ x+i_ 4 , is…
• A solution of the differential equation ( d y d x )^ 2 -x d y d x +y=0 is,
• A tangent to the curve y = f (x) cuts the line y = x at a point which is at a distance of 1 unit from y–axis. The…
• The differential equation representing the family of curves y ^ 2 =2 c ( x + c ) . Where c>0 , is a parameter is of…
• The order and degree of the following differential equation ( d ^ 2 ~s dt ^ 2 )^ 2 +3 ( ds dt )^ 3 +4=0 are
• The Solution of the equation (1– x 2 ) dy + xy dx = xy 2 dx is-
• The solution of differential equation (2x – 10 y 3 ) dy dx + y = 0 is :
• If a curve passes through the point (1, -2) and has slope of the tangent at any point (x, y) on it as x^ 2 -2 y x …
• The solution of the differential equation y dx + (x + x 2 y) dy = 0 is
• The solution of the differential equation (x-1) d y+y d x=x(x-1) y^ 1 3 d x , is
• The solution of the differential equation (x y^ 4 +y ) d x-x d y=0 is,
• The slope of the tangent at (x, y) to a curve passing through (2, 1) is x^ 2 +y^ 2 2 x y , then the equation of the…
• The solution of the following differential equation x ( y x )(y d x+x d y)=y ( y x )(x d y-y d x) is :
• d y d x = x y x^ 2 +y^ 2 ; y(1)=1 then a value of x satisfying y(x) = e is :
• Let a solution y=y(x) of the differential equation x x^ 2 -1 d y-y y^ 2 -1 d x=0 satisfy y(2)= 2 3 . Statement - 1 …
• Solution of the differential equation y (2 x^ 4 +y ) d y d x = (1-4 x y^ 2 ) x^ 2 is given by :
• The order of the differential equation satisfying 1-x^ 2 + 1-y^ 2 =a(x-y) ; 5 ,
• The general solution of the differential equation y [x^ 2 y+e^ x ] d x-e^ x d y=0 is,
• The degree of the differential equation corresponding to the family of curves y=a(x+a)^ 2 , where a is an arbitrary…
• The solution of the differential equation (1+y^ 2 )+ (x-e^ ^ -1 y ) d y d x =0 is

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