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,
Mathematics · JEE Main · NTA Exams — Differential Equations
The solution of the equation \(x^{2} \frac{d^{2} y}{d x^{2}}=\log x\) when \(\mathbf{x}=1_{1} \mathbf{y}=\mathbf{0}\) and \(\frac{d y}{d x}=-1\) is,
- \(\frac{1}{2}(\log x)^{2}+\log x\)
- \(\frac{1}{2}(\log x)^{2}-\log x\)
- \(-\frac{1}{2}(\log x)^{2}+\log x\)
- \(-\frac{1}{2}(\log x)^{2}-\log x\)
Answer
(D) - 1 2 ( x)^ 2 - x
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The solution of the differential equation (e^ -2 x - y x ) d x d y =1 is given by
- If φ (x) is a differentiable function, then the solution of the differential equation d y+ y ^ (x)- (x) ^ (x)…
- The solution of the differential equation, d y d x =(x-y)^ 2 , where y(1)=1 , is:
- The differential equation which represents the family of curves y = c _ 1 e ^ c _ 2 x where c 1 and c 2 are…
- 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 equation of the curve for which the tangent at P (x, y) cuts the y – axis at (0, y 3 ) is
- The degree of the differential equation corresponding to the family of curves y=a(x+a)^ 2 , where a is an…
- The solution of the differential equation x d y d x =y-x ( y x ) is ,
More Differential Equations questions · Browse all practice questions