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

Solve dy/dx-2y=e3x with y(0)=0 and find y(1).

1. 12.7
2. 20.09
3. 7.39
4. 14.78

Answer

A. 12.7

Solution

The integrating factor is e-2x: d/dx≤ft(ye-2x )=ex ye-2x=ex+C. y(0)=0 C=-1, so y=e3x-e2x and y(1)=e3-e2 12.70.

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