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

Find the general solution of y''+4y=8e2x.

  1. y = C1 2 x + C2 2 x + 2 e2 x
  2. y = C1 2 x + C2 2 x + e2 x2
  3. y = C1 2 x + C2 2 x + x e2 x
  4. y = C1 2 x + C2 2 x + e2 x

Answer

D. y = C1 2 x + C2 2 x + e2 x

Solution

Complementary: yc=C1 2x+C2 2x. Try yp=Ae2x: 4A+4A=8 A=1. So y=C1 2x+C2 2x+e2x.

More Nonhomogeneous Second-Order Equations questions

  1. Find the general solution of y''-3y'+2y=4x.
  2. Find the general solution of y''+y'-2y=6.
  3. Find the general solution of y''-y=4.
  4. Use variation of parameters to solve y''+y= x for 0<x< π2.
  5. Find the general solution of y''-4y'+4y=e2x.
  6. Find the general solution of y''+y= x.
  7. Solve y''+y=2 with y(0)=0 and y'(0)=0, and find y(π).
  8. Find the general solution of y''+3y'+2y=12x2.
  9. Find the general solution of y''-2y'-3y=6e-x.

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