## Differential Equations and Linear Algebra (4th Edition)

The first order linear equation must be in the form of $y'+p(x)y=q(x)$, therefore, the equation is rewritten as $y'+\frac{y}{x}=x$. This means that $p(x)=\frac{1}{x}$. The integrating factor is equal to $e^{\int p(x)dx}$, which is $e^{\int \frac{dx}{x}}=e^{ln(x)}=x$. This doesn't match the integrating factor of $I(x)=x+5$.