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

Find the general solution of dy/dx-y=x.

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

Answer

B. y = C ex - x - 1

Solution

The integrating factor is e-x: d/dx≤ft(ye-x )=xe-x ye-x=-xe-x-e-x+C y=Cex-x-1.

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