This problem is split into several steps. All refer to the differential equation

$5\frac{dy}{dx}=-7e^{4x}-6y$

Step $1$: Rewrite in standard form

Rewrite the equation in the form $\frac{dy}{dx}+P(x)y=Q(x).$ If this is not a linear equation, enter "DNE" for both functions.

$P(x)=\frac{6}{5}$

and

$Q(x)=\frac{7}{5}$

Step $2$: Find the integration factor

Find the integration factor $(x)=e^{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}P(x)dx}.$

$(x)=,$grad

Step $3$: Multiply and integrate

Multiply both sides of the equation $($as rewritten in standard form$)$ by the integration factor, and integrate:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x)(y^{\text{'}}+P(x)y)dx=,(1)+C_1,$ and

Step $4$: Solve for y

Solve for the general solution $y$ from your answer above. Enter any arbitrary constant as $C.$

$y(x)=$

$$