Question

If $p$ and $q$ are order and degree of differential equation $y^2\left(\frac{d^{2}y}{d{x}^2}\right)+3x{\left(\frac{dy}{dx}\right)}^{\frac{1}{3}}+x^2{y}^2=\sin x$ then find $p+q$

Answer 1

Solution:-

Order of differential equation:-

The order of a differential equation is the order of the highest order derivative present in the equation.

Degree of differential equation:-

The degree of a differential equation is the power of the highest order derivative in the equation.

$y^2\left(\frac{d^{2}y}{d{x}^2}\right)+3x{\left(\frac{dy}{dx}\right)}^{\frac{1}{3}}+x^2{y}^2=\sin x$

$\therefore p=$ order of equation $=2$

$q=$ degree of equation $=1$

$\therefore p+q=1+2=3$

Hence, the correct answer is 3.