Answers to Selected Exercises 551- a. 3x^2 /2 b. 4xe-^2 x
c. - 2x cos v'3x d. e- x + x - l
e. ex cos 2x f. ex sin 2xg. 4(cosx-1) h. 2e-x cos x + 3e-x sin x
i. x + 2 sinhx j. 3e^2 x coshx
Exercises 5.2 Using the Laplace Transform and Its Inverse to Solve
Initial Value Problems1.- y = Ae-^2 x +^2
5.. 1
y = Acos3x + Bsm3x -
3
xcos3x
7. y = Aex + Bxex + C + Dx - x^2 ex + x^3 ex /6 - 9x^2 - 2x^3 - x^4 /4
9.- y = ( -33 cos 3x + 8 sin 3x + 3x + 6) /2 7
- y = ex cos x - x^2 /2 - x
Exercises 5.3 Convolution and the Laplace Transform
1. h(x) = (1 - cos3x)/9
- h(x) = [(3x - l)e^2 x + e-x]/9
- h(x) = (2 sin 2x - cos 2x + ex)/5
- y = -3 + 5e^2 x
9. y = (1 - cos3x)/9
11. y = e2x - e-x
- y = 3xex - 3ex + cosx