What is the solution for y^{''}+2y^'+2y=5sin(t)+5cos(t) ?

The solution for y^{''}+2y^'+2y=5sin(t)+5cos(t) is y=e^{-t}(c_{1}cos(t)+c_{2}sin(t))+3sin(t)-cos(t)

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y^{''}+2y^'+2y=5sin(t)+5cos(t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 sin (t) + 5 cos (t)

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 3 sin (t) - cos (t)

Solution steps

y^{''} (t) + 2 y^{'} (t) + 2 y = 5 sin (t) + 5 cos (t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 3 sin (t) - cos (t)

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 3 sin (t) - cos (t)

y^{^{''}} - 16 y^{^{'}} + 64 y = 5 t e^{8 t}

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10

y^{^{''}} - y^{^{'}} - 2 y = sin (t)

x^{^{''}} + 14 x^{^{'}} + 98 x = 1960

y^{^{''}} + 4 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

What is the solution for y^{''}+2y^'+2y=5sin(t)+5cos(t) ?
The solution for y^{''}+2y^'+2y=5sin(t)+5cos(t) is y=e^{-t}(c_{1}cos(t)+c_{2}sin(t))+3sin(t)-cos(t)