What is the solution for y^{''}+7y^'+12y=340cos(t) ?

The solution for y^{''}+7y^'+12y=340cos(t) is y=c_{1}e^{-3t}+c_{2}e^{-4t}+14sin(t)+22cos(t)

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y^{''}+7y^'+12y=340cos(t)

y^{^{''}} + 7 y^{^{'}} + 12 y = 340 cos (t)

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + 14 sin (t) + 22 cos (t)

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = 340 cos (t)

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + 14 sin (t) + 22 cos (t)

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + 14 sin (t) + 22 cos (t)

What is the solution for y^{''}+7y^'+12y=340cos(t) ?
The solution for y^{''}+7y^'+12y=340cos(t) is y=c_{1}e^{-3t}+c_{2}e^{-4t}+14sin(t)+22cos(t)