DHS 16.2 - Option 21. Decisions Ryabushko AP

1. Solve a linear differential equation using the operator method
αẍ + βẋ + γx = f(t), x(t0) = A, ẋ(t0) = B
The function f(t) and values of coefficients α, β, γ, t0, x(t0), ẋ(t0) are taken from the table. 16.4
1.21. α = 1, β = 4, γ = 4, f(t) = 9et, t0 = 0, x(t0) = 0, ẋ(t0) = 0
1.21. ẍ + 4ẋ + 4x = 9, x(0) = 0, ẋ(0) = 0

2. Solve the system of linear differential equations by the operator method
Table of functions f1(t), f2(t) and values ak, bk, ck, dk (k=1, 2), A, B, x(0), y(0). 16.5
2.21. a1 = 1, b1 = 0, c1 = 2, d1 = 4, f1(t) = 4t+1, a2 = 0, b2 = 1, c2 = 1, d2 = −1, f2(t) = (3/ 2)t2, x(0) = 0, y(0) = 0