# Determine order and degree(if defined) of differential equation

Question:

Determine order and degree(if defined) of differential equation $y^{\prime}+y=e^{x}$

Solution:

$y^{\prime}+y=e^{x}$

$\Rightarrow y^{\prime}+y-e^{x}=0$

The highest order derivative present in the differential equation is $y^{\prime}$. Therefore, its order is one.

The given differential equation is a polynomial equation in $y^{\prime}$ and the highest power raised to $y^{\prime}$ is one. Hence, its degree is one.