Question

Degree of the differential equation
$\frac{d^{4}y}{d{x}^4}+(\frac{d^{3}y}{d{x}^3}{)}^2+(\frac{d^{2}y}{d{x}^2}{)}^3+(\frac{dy}{dx}{)}^4=0$ is ___

Answer 1

Degree of a differential equation is defined as the highest power of highest derivative in it.
The highest derivative present in the equation is fourth derivative of $y$ with respect to $x$. So the degree will be the power associated with $\frac{d^{4}y}{d{x}^4}$. which is 1. Some of us may think that the degree is 4 after seeing the term $(\frac{dy}{dx}{)}^4$. We should look at powers only after finding the highest derivative.