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

Find the general solution of y''+y'-2y=6.

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

Answer

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

Solution

Complementary: r2+r-2=0 r=1,-2. Try yp=A: -2A=6 A=-3. So y=C1ex+C2e-2x-3.

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