What is the solution for y^{''}+7y^'+10y=-10+e^{4t} ?

The solution for y^{''}+7y^'+10y=-10+e^{4t} is y=c_{1}e^{-2t}+c_{2}e^{-5t}-1+1/54 e^{4t}

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y^{''}+7y^'+10y=-10+e^{4t}

y^{^{''}} + 7 y^{^{'}} + 10 y = - 10 + e^{4 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - 1 + \frac{1}{54} e^{4 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 10 y = - 10 + e^{4 t}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - 1 + \frac{1}{54} e^{4 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - 1 + \frac{1}{54} e^{4 t}

y^{^{''}} - y = cos (2 x)

y^{^{''}} + 2 y^{^{'}} + 2 y = (e^{(- x)}) \cdot cos (x)

y^{^{''}} - 3 y^{^{'}} - 4 y = x e^{x} + 2 cos (x) - sin (x)

D (D - 1)^{3} y = (x^{2} + 2 x) e^{x}

y^{^{''}} + 4 y = \frac{cos ( 2 x )}{2}

What is the solution for y^{''}+7y^'+10y=-10+e^{4t} ?
The solution for y^{''}+7y^'+10y=-10+e^{4t} is y=c_{1}e^{-2t}+c_{2}e^{-5t}-1+1/54 e^{4t}