Differential equation

Question

Show that is a solution of the differential equation y' + 2y = 2e^x.

Answer 1

Step 1:

The function is .

Apply derivative on each side with respect to .

Use sum rule of derivative : .

.

Step 2:

The differential equation is .

Consider .

Substitute the values of and in .

Simplify the expression.

           

Rewrite the expression.

           

.

Solution :

is the solution of differential equation .