If is twice differentiable function of

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If yy is twice differentiable function of xx, then the expression (1−x2)⋅d2ydx2−xdydx+y by means of the\text{expression } (1-x^2) \cdot \frac{d^2 y}{dx^2} - x \frac{dy}{dx} + y \text{ by means of the} transformation x=sin⁡t in terms of t is d2ydt2+λy.\text{transformation } x = \sin t \text{ in terms of } t \text{ is } \frac{d^2 y}{dt^2} + \lambda y. Thus, λ\lambda is .....

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