What is the solution for y^{''}-7y^'+10y=9cos(t)+7sin(t) ?

The solution for y^{''}-7y^'+10y=9cos(t)+7sin(t) is y=c_{1}e^{5t}+c_{2}e^{2t}+cos(t)

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y^{''}-7y^'+10y=9cos(t)+7sin(t)

y^{^{''}} - 7 y^{^{'}} + 10 y = 9 cos (t) + 7 sin (t)

y = c_{1} e^{5 t} + c_{2} e^{2 t} + cos (t)

Solution steps

y^{''} (t) - 7 y^{'} (t) + 10 y = 9 cos (t) + 7 sin (t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{2 t} + cos (t)

y = c_{1} e^{5 t} + c_{2} e^{2 t} + cos (t)

y^{^{''}} - y = cosh (x), y (0) = 2, y^{^{'}} (0) = 12

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{4 t}

y^{^{''}} + 2 y^{^{'}} + 2 y = 3, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- x}

(4 d^{2} + 12 d + 9) y = 2022

What is the solution for y^{''}-7y^'+10y=9cos(t)+7sin(t) ?
The solution for y^{''}-7y^'+10y=9cos(t)+7sin(t) is y=c_{1}e^{5t}+c_{2}e^{2t}+cos(t)