DHS 16.2 - Option 13. Decisions Ryabushko AP
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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
1.13. α = 1, β = 0, γ = −4, f(t) = 4t, t0 = 0, x(t0) = 1, ẋ(t0) = 0
1.13. ẍ − 4x = 4t, x(0) = 1, 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
2.13. a1 = 1, b1 = 0, c1 = 1, d1 = −3, f1(t) = 0, a2 = 0, b2 = 1, c2 = −1, d2 = −1, f2(t) = et, x (0) = 1, y(0)=1
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
1.13. α = 1, β = 0, γ = −4, f(t) = 4t, t0 = 0, x(t0) = 1, ẋ(t0) = 0
1.13. ẍ − 4x = 4t, x(0) = 1, 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
2.13. a1 = 1, b1 = 0, c1 = 1, d1 = −3, f1(t) = 0, a2 = 0, b2 = 1, c2 = −1, d2 = −1, f2(t) = et, x (0) = 1, y(0)=1
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