Mathematics - Differential Equation Question with Solution | TestHub

$A{x}^2+B{y}^2=1$ ...(1) $Ax+By\frac{dy}{dx}=0$ ...(2) $A+By\frac{d^{2}y}{d{x}^2}+B{\left(\frac{dy}{dx}\right)}^2=0$ ...(3) $x\left\{-By\frac{d^{2}y}{d{x}^2}-B{\left(\frac{dy}{dx}\right)}^2\right\}+By\frac{dy}{dx}=0$ Dividing both sides by $-\mathrm{B}$, we get $xy\frac{d^{2}y}{d{x}^2}+x{\left(\frac{dy}{dx}\right)}^2-y\frac{dy}{dx}=0$ Which is a DE of order 2 and degree 1