Question

Write the order of the differential equation :
$\log \left(\frac{d^{2}y}{d{x}^2}\right)={\left(\frac{dy}{dx}\right)}^3+x$

Answer 1

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

$\log \left(\frac{d^{2}y}{d{x}^2}\right)-{\left(\frac{dy}{dx}\right)}^3+(-x)=0$

$\log \left(\frac{d^{2}y}{d{x}^2}\right)-{\left(\frac{dy}{dx}\right)}^3-x=0$

$\log y^{11}-(y^{\prime }{)}^3-x=0$

Highest order of dervitative $=2$

$\therefore$ order $=2$.