Engineering Board Exam Reviewer · Linear First-Order Differential Equations · medium

Solve the linear differential equation dy/dx+y=ex.

1. y= 12ex+Ce-x
2. y=ex+Ce-x
3. y= 12e2x+C
4. y=Ce-x

Answer

A. y= 12ex+Ce-x

Solution

The integrating factor is =ex. Then (yex)'=e2x yex= 12e2x+C y= 12ex+Ce-x.

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