Reference no: EM131072802
1. Solve the following differential equations:
A. D (D +3)3 (D2 +9)(D2 -2x-8)y = 0
B. ym-4ym-9y'+36y=0
C. ym-4y'= x +3 cos x + e-2x [Hint: Use undetermined coefficients]
D. y" +4y' +4y = X-2e-2x with x > 0 [Hint: Use variation of parameters]
2. Determine an annihilator for x2e3x + 5 cos 2x.
3. Convert the following system to a first-order system:
d2x/dt2-3dy/dt+x=sint,
d2y/dt2 - tdx/dt-e'y = t2
4. Solve the following linear system of differential equations:
x1'= x1 + 2x2
x2'= 4x1 + 3x2
5. Solve the following nonhomogeneous linear system of differential equations:
x1' = x1+ 2x2 +12e3t
x2' = 4x1 +3x2 +18e2t
6. Compute the Laplace transforms of the following functions:
A. e5t sin 3t
B. u2 (t)sin (5 (t - 2))
7. Compute the inverse Laplace transforms of the following functions:
A. 7e-21/s2 +4
B. 3s+2 /(s -1)(s -2)
8. Solve the following initial-value problem by using Laplace transforms:
yn-4y=12e2t with y(0) = 2 and y'(0) = 3.
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