We are given that dy/dx= sin(y)/x. Find the expression for d^2y/dx^2 in terms of x and y

Question

We are given that dy/dx= sin(y)/x. Find the expression for d^2y/dx^2 in terms of x and y

Answer 1

dy/dx = sin y / x

d²y / dx² = [x(cosy)(dy/dx) - siny] / x² = [x(cosy)(siny / x) - siny] / x² = [(cosy)(siny) - siny] / x²

= siny (cosy - 1) / x²

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