Engineering Board Exam Reviewer · Nonhomogeneous Second-Order Equations · easy

Find the general solution of y''-y=4.

1. y = C1 ex + C2 e- x - 4
2. y = C1 ex + C2 e- x + 4
3. y = C1 ex + C2 e- x - 4 x
4. y = C1 x + C2 x - 4

Answer

A. y = C1 ex + C2 e- x - 4

Solution

Complementary: yc=C1ex+C2e-x. Try yp=A: -A=4 A=-4. So y=C1ex+C2e-x-4.

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1. Use variation of parameters to solve y''+y= x for 0<x< π2.
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