Question

Which of the following equation is non-linear

• A. $\frac{dy}{dx}=cosx$
• B. $\frac{d^{2}y}{d{x}^2}+y=0$
• C. $dx+dy=0$
• D. $x\frac{dy}{dx}+\frac{3}{\frac{dy}{dx}}=y^2$

Answer 1

The correct option is D

$x\frac{dy}{dx}+\frac{3}{\frac{dy}{dx}}=y^2$

$x\frac{dy}{dx}+\frac{3}{\left(dy/dx\right)}=y^2\Rightarrow x{\left(\frac{dy}{dx}\right)}^2-y^2\frac{dy}{dx}+3=0$
Hence it is a non-linear differential equation.