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

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

1. y = ≤ft(C + x ) ex
2. y = C e- x + e- x
3. y = ≤ft(C + x22 ) e- x
4. y = ≤ft(C + x ) e- x

Answer

D. y = ≤ft(C + x ) e- x

Solution

The integrating factor is ex: d/dx(yex)=1 yex=x+C y=(x+C)e-x.

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