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

Solve dy/dx+3y=6, given y(0)=1.

1. y=2-e-3x
2. y=2+e-3x
3. y=2e-3x-1
4. y=1-e-3x

Answer

A. y=2-e-3x

Solution

Integrating factor e3x: (ye3x)'=6e3x ye3x=2e3x+C y=2+Ce-3x. Using y(0)=1: C=-1, so y=2-e-3x.

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