Question

Find the order and degree of the differential equation $x^{\frac{1}{2}}{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}+x\cdot \frac{dy}{dx}+y=0$

Answer 1

We have, $x^{\frac{1}{2}}{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}+x\cdot \frac{dy}{dx}+y=0$

$\Rightarrow x^{\frac{1}{2}}{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}=-x\cdot \frac{dy}{dx}-y$

Now take power 6 on both sides,

$x^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^2={(x\frac{dy}{dx}+y)}^6$

So degree $=2$

and order $2$