If is a function of

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If yy is a function of xx, then d2ydx2+y⋅dydx=0\frac{d^2 y}{dx^2} + y \cdot \frac{dy}{dx} = 0 . If xx is a function of yy , then the equation becomes (1) d2xdy2−x⋅dxdy=0\frac{d^2 x}{dy^2} - x \cdot \frac{dx}{dy} = 0 (2) d2xdy2+y(dxdy)3=0\frac{d^2 x}{dy^2} + y \left( \frac{dx}{dy} \right)^3 = 0 (3) d2xdy2−y(dxdy)2=0\frac{d^2 x}{dy^2} - y \left( \frac{dx}{dy} \right)^2 = 0 (4) d2xdy2−x(dxdy)2=0\frac{d^2 x}{dy^2} - x \left( \frac{dx}{dy} \right)^2 = 0

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