Answer to Question #244277 in Differential Equations for Jac

Question

Solve the differential equation of the following linear differential equations. Show complete solution.

dy/dx + y = e^2x

Answer 1

The integration factor: $\mu(x)=e^x$

$$e^x\dfrac{dy}{dx}+e^xy=e^{3x}$$

$$d(e^xy)=e^{3x}dx$$

Integrate

$$e^xy=\int e^{3x}dx$$

$$e^xy=\dfrac{1}{3} e^{3x}+C$$

$$y=\dfrac{1}{3}e^{2x}+Ce^{-x}$$