DHS 16.2 - Option 2. 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
1.2. α = 0, β = 1, γ = 2, f(t) = 5cost, t0 = 0, x(t0) = 2, ẋ(t0) = −3
1.2. ẋ + 2x = 5cost, x(0) = 2, ẋ(0) = −3

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
2.2. a1 = 0, b1 = 1, c1 = −1, d1 = −2, f1(t) = cost, a2 = 1, b2 = 0, c2 = 2, d2 = 1, f2(t) = sint, x( 0) = 0, y(0) = 0