What is the solution for y^{''}+7y^'+10y=3e^{4t} ?

The solution for y^{''}+7y^'+10y=3e^{4t} is y=c_{1}e^{-2t}+c_{2}e^{-5t}+1/18 e^{4t}

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y^{''}+7y^'+10y=3e^{4t}

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 e^{4 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{1}{18} e^{4 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 10 y = 3 e^{4 t}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{1}{18} e^{4 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{1}{18} e^{4 t}

\frac{d}{d x} (A x e^{x^{2}})

\int (2 sec^{2} (x) - x^{5}) d x

\int (x sin (y)) d y

x \to - 5 lim (\frac{8}{( x + 5 ) ^{6}})

f (x) = 5 e^{e}

What is the solution for y^{''}+7y^'+10y=3e^{4t} ?
The solution for y^{''}+7y^'+10y=3e^{4t} is y=c_{1}e^{-2t}+c_{2}e^{-5t}+1/18 e^{4t}