Question

Write the sum of the order and degree of the following differential equation: $\frac{d}{dx}\left\{{\left(\frac{dy}{dx}\right)}^3\right\}=0$.

Answer 1

By using chain rule to evaluate the derivative on the left hand side, we get:

$\frac{d}{dx}$ {${\left(\frac{dy}{dx}\right)}^3$} $=0.$

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

The order of this differential equation is $2$ because the highest order derivative appearing in the equation is second order.

The degree is the power of this highest order derivative. In this case degree is $1.$

So, the answer is $2+1=3.$