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

Find the general solution of y''-3y'+2y=4x.

1. y = C1 ex + C2 e2 x + 2 x - 3
2. y = C1 ex + C2 e2 x + 4 x + 6
3. y = C1 ex + C2 e2 x + 2 x + 3
4. y = C1 ex + C2 e2 x + 2 x + 3/2

Answer

C. y = C1 ex + C2 e2 x + 2 x + 3

Solution

Complementary: r=1,2. Try yp=Ax+B: -3A+2Ax+2B=4x A=2 and -6+2B=0 B=3. So y=C1ex+C2e2x+2x+3.

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