Holly Guerrero

2022-01-20

Is the following is linear equation?
$x\frac{dy}{dx}-4y={x}^{6}{e}^{x}$

Neil Dismukes

Expert

First order linear differential equation: A differential equation of the form $\frac{dx}{dy}+P\left(x\right)y=Q\left(x\right)$ is called first order linear differential equation.
Here we have given,
$x\frac{dy}{dx}-4y={x}^{6}{e}^{x}$
$⇒\frac{dy}{dx}-\frac{4}{x}y={x}^{5}{e}^{x}$
Which is of the form
Hence, the given equation is a first order linear differential equation.

William Appel

Expert

Linear and first order, here $P=-\frac{4}{x}$ and $Q=6{e}^{x}$