Question

Obtain differential equation from the relation $A{x}^2+B{y}^2=1$, where A and B are constants

Answer 1

$A{x}^2+B{y}^2=1$

By differentiating, we get

$2Ax+2By\frac{dy}{dx}=0$-Equation 1

By differentiating, we get

$2A+2By\frac{d^{2}y}{d{x}^2}+2B(\frac{dy}{dx}{)}^2=0$

$A=-B(y\frac{d^{2}y}{d{x}^2}+(\frac{dy}{dx}{)}^2)$

Putting value of A in equation 1, we get

$-x(y\frac{d^{2}x}{d{x}^2}+(\frac{dy}{dx}{)}^2)+y\frac{dy}{dx}=0$

$y\frac{dy}{dx}-x(\frac{dy}{dx}{)}^2-xy\frac{d^{2}y}{d{x}^2}=0$