Question

What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?

Options

• \[(1-x^2)\frac{dy}{dx}-x\frac{d^2y}{dx^2}=0\]

• \[\frac{d^2y}{dx^2}-x\frac{dy}{dx}=0\]

• \[(1-x^2)\frac{d^2y}{dx^2}-x\frac{dy}{dx}=0\]

• \[(1-x^2)\frac{d^2y}{dx^2}+x\frac{dy}{dx}=0\]

Answer 1

Multiplication by \[\sqrt{1-x^2}\] changes the first coefficient to \[1-x^2\]. The remaining term becomes \[-x\frac{dy}{dx}\], giving the stated differential equation.