Solution of IDZ Ryabushko 16.2 - Variant 4

Section: Chapter 16. Operational Calculus
Topic: Operator method for solving differential equations
Description: Solving linear differential equations and systems with constant coefficients using the operator method (Laplace transform) under given initial conditions.

Tasks:
1. Solve the linear differential equation αẍ + βẋ + γx = f(t), x(t₀) = A, ẋ(t₀) = B by the operator method. Take the function f(t) and the values of the coefficients α, β, γ, t₀, x(t₀), ẋ(t₀) from Table 16.4.
2. Solve the system of linear differential equations by the operator method. Take the functions f₁(t), f₂(t) and the values aₖ, bₖ, cₖ, dₖ (k = 1, 2), A, B, x(0), y(0) from Table 16.5.

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