Differential Equations — practice questions
63 curated practice questions from Differential Equations (Mathematics JEE Advanced, NTA Exams) — 20 medium, 43 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.
- The solution of primitive equation ( x 2 + y 2 ) dy = xy dx , is y = y ( x ). If y (1) = 1 and y ( x 0 ) = e , then x 0…
- The order of the differential equation whose general solution given by y = ( c 1 + c 2 ) cos( x + c 3 ) – c_ 4 e^ x+c_…
- The differential equation of all the ellipses centred at the origin and having their axes as co-ordinate axes is :
- Let f : [0, ∞) → be a continuous function such that f(x)=1-2 x+ _ 0 ^ x e^ x-t f(t) d t for all x ∈[0, ∞). Then…
- Explanation:tion of the differential equation 3x 2 y 2 + cos (xy) – xy sin (xy) + dy dx (2x 3 y – x 2 sin (xy)) = 0 is
- If _ a ^ x t y(t) d t = x 2 + y (x) then y as a function of x is
- The substitution y = z α transforms the differential equation (x 2 y 2 – 1)dy + 2xy 3 dx = 0 into a homogeneous…
- The Explanation:tion of p^ 2 +(2 y x) p=y^ 2 where p= d y d x is
- The equation of the curve satisfying the equation x(1-x y) d y d x +y=0 and passing through (1, 1 e ) is
- A solution curve of the differential equation (x^ 2 +x y+4 x+2 y+4 ) d y d x -y^ 2 =0, x>0 passes through the point (1…
- Consider the family of all circles whose centres lie on the straight line y = x . If this family of circles is…
- The function satisfying the equation f(x)=- _ 0 ^ x f(t) t d t+ _ 0 ^ x (t-x) d t, where x (- 2 , 2 ) is :
- The Explanation:tion of the differential equation x dx + y dy + x d y-y d x x^ 2 +y^ 2 =0 is
- For any real numbers α and β, let y_ , (x), x R , be the solution of the differential equation d y d x + y=x e^ x …
- Explanation:tion of differential equation dy dx = y + _ 0 ^ 1 ydx , y (0) = 1 is :
- The Explanation:tion of the differential equation dy dx = y x + ( y / x ) ^ ( y / x ) is
- If x 2 + y 2 = 1, then
- Explanation:tion of the differential equation y (xy + 2x 2 y 2 ) dx + x (xy – x 2 y 2 ) dy = 0 is given by
- A curve passes through the point (1, 6 ) . Let the slope of the curve at each point ( x , y ) be y x + ( y x ), x > 0 …
- Consider the differential equation e x (ydx – dy) = e –x (ydx + dy). Let y = f(x) be a particular Explanation:tion to…
- The equation of curve for which y intercept of tangent varies as cube of the abscissa of point of contact, is
- For the primitive integral equation ydx + y 2 dy = x dy ; x ∈ R , y > 0, y = y ( x ), y (1) = 1, then y (–3) is
- If y ( x ) satisfies the differential equation y ′ – y tan x = 2 x sec x and y (0) = 0, then
- Explanation:tion of the differential equation : (3 tan x + 4 cot y – 7) sin 2 y dx – (4tan x + 7 cot y – 5) cos 2 xdy =…
- Explanation:tion of differential equation (x 2 + y 2 + a 2 ) y dy dx + x (x 2 + y 2 – a 2 ) = 0 is
- The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve…
- The Explanation:tion of the differential equation (x 3 – 3xy 2 ) dx = (y 3 – 3x 2 y) dy is
- The differential equation whose general Explanation:tion is given by, y= (c_ 1 (x+c_ 2 ) )- (c_ 3 e^ (-x+c_ 4 ) )+ (c_…
- The latus rectum of the conic passing through the origin and having the property that normal at each point (x, y)…
- The orthogonal trajectories of the family of circle given by x 2 + y 2 – 2ay = 0 (a is parameter), is :
- The orthogonal trajectories of the family of curves a n–1 y = x n are given by (a is the arbitary constant)
- Let f : (0, ∞) → R be a differentiable function such that f^ (x)=2- f(x) x for all x ∈ (0, ∞) and f (1) ≠ 1. Then
- Let a solution y = y ( x ) of the differential equation x x^ 2 -1 d y-y y^ 2 -1 d x=0 satisfies y(2)= 2 3 . Statement …
- The equation of the curve passing through origin if the middle point of the segment of its normal from any point of the…
- A Explanation:tion of the differential equation ( d y d x )^ 2 -x d y d x +y=0 is:
- The function y = f ( x ) is the solution of the differential equation d y d x + x y x^ 2 -1 = x^ 4 +2 x 1-x^ 2 in (–1…
- A function y = f (x) satisfies (x + 1) . f ′ (x) – 2 (x 2 + x) f (x) = e ^ x ^ 2 ( x +1) , x>-1 If f (0) = 5 , then f…
- If y = y ( x ) satisfies the differential equation 8 x ( 9+ x ) d y=( 4+ 9+ x )^ -1 d x, x>0 and y(0)= 7 , then y(256)=
- Explanation:tion of the differential equation x d x+ y d y x d x- y d y = y^ 3 x^ 3 is given by
- The Explanation:tion of the differential equation d y d x + x(3 y-7 x-3) y(3 x-7 y+7) =0 is
- The Explanation:tion of the differential equation d ^ 2 y dx ^ 2 = sin3x + e x + x 2 when y’(0) = 1 and y (0) = 0 is
- Explanation:tion of differential equation x^ 3 d y d x =y^ 3 +y^ 2 y^ 2 -x^ 2 is
- The differential equation d y d x = 1-y^ 2 y determines a family of circles with
- If the function y = e 4x + 2e –x is a Explanation:tion of the differential equation d^ 3 y d x^ 3 -13 d y d x y =K then…
- If y ( t ) is a solution of and y (0) = –1, then y (1) is equal to
- An inverted conical tank of 2 m radius and 4 m height is initially full of water, has an outlet at bottom. The outlet…
- The curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the…
- The equation of the curve for which any tangent intersects the y–axis at the point equidistant from the point of…
- A function y = f (x) satisfies the differential equation dy dx – y = cos x – sin x with initial condition that y is…
- Explanation:tion of the differential equation y 2 (ydx + 2xdy) – x 2 (2ydx + xdy) = 0 is
- Explanation:tions of the differential equation ( d y d x )^ 2 - d y d x (e^ x +e^ -x )+1=0 are given by
- If y = y ( x ) and 2+ x y+1 ( d y d x )=- x, y(0)=1 , then y ( 2 ) equals
- The equation of the curve satisfying the differential equation d^ 2 y d x^ 2 (x^ 2 +1 )=2 x d y d x passing through the…
- Consider the differential equation e x (ydx – dy) = e –x (ydx + dy). Let y = f(x) be a particular Explanation:tion to…
- The differential equation representing the family of curves y^ 2 =2 c(x+ c ) , where c is a positive parameter, is of
- For x ∈ R , let the function y ( x ) be the solution of the differential equation d y d x +12 y= ( 12 x ), y(0)=0 …
- A curve y = f (x) passing through the point (1, 1 e ) satisfies the differential equation dy dx + x e^ - x^ 2 2 = 0…
- Explanation:tion of the differential equation d y d x + ( x+y 2 )= x-y 2 is
- Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate…
- The Explanation:tion of d y d x = x^ 2 +y^ 2 +1 2 x y satisfying y(1) = 1 is given by
- Let y ( x ) be a solution of the differential equation (1 + e x ) y ′ + ye x = 1 . If y (0) = 2, then which of the…
- Explanation:tion of the differential equation (e^ x^ 2 +e^ y^ 2 ) y d y d x + e ^ x ^ 2 ( xy ^ 2 - x ) = 0, is
- A curve passing through (2, 3) and satisfying the differential equation _ 0 ^ x t y(t) d t = x 2 y (x), (x >0) is