Answer
$y=\cos x$ is not a solution to the given differential equation.
Work Step by Step
We will find $y'$ and substitute it along with $y$ into the given differential equation.
$$y'=(\cos x)' = -\sin x.$$
Now by substituting we get:
The Left side:
$$xy'-2y=-x\sin x-2\cos x$$
The Right side is just
$$x^3e^x.$$
The Left side is NOT equal to the right side for every $x$ so $y=\cos x$ is not a solution to the given differential equation.
