Question

Find the sum of the order and degree of the differential equation $\frac{d^{2}y}{d{x}^2}+\sqrt[3]{3\frac{dy}{dx}}+(x+1)=0$.

Answer 1

Given the differential equation is

$\frac{d^{2}y}{d{x}^2}+\sqrt[3]{3\frac{dy}{dx}}+(x+1)=0$

or, $\frac{d^{2}y}{d{x}^2}+x+1=-\sqrt[3]{3\frac{dy}{dx}}$

or, ${(\frac{d^{2}y}{d{x}^2}+x+1)}^3=-\frac{dy}{dx}$.

From this equation it is clear that the highest order term involved in the equation is $\frac{d^{2}y}{d{x}^2}$ and the power of this term is $3$.

So the degree of the differential equation is $3$ and the order is $2$.

So sum of the order and the degree of the differential equation is $3+2=5$.