Answer to Question #244747 in Differential Equations for Jac

Question

Solve the differential equation of the following linear differential equations. Show step-by-step procedures.

dy/dx + y = e^2x

Answer 1

dy/dx + y = e^2x

Step 1:

dy/dx + Py = Q

P = 1, Q = e^2x

Step 2:

I.F. = e^{integration Pdx}

I.F. = e^{integration dx}

I.F. = e^x

Step 3:

y * I.F. = Integration Q * I.F. dx + c

y * e^x = Integration e^2x * e^x dx + c

ye^x = Integration e^3x dx + c

ye^x = e^3x dx + c

Dividing by e^x

y = e^2x + ce^-x