What is the solution for y^{''}+3y^'+2y=30e^{2x} ?

The solution for y^{''}+3y^'+2y=30e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+5/2 e^{2x}

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y^{''}+3y^'+2y=30e^{2x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 30 e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{5}{2} e^{2 x}

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 30 e^{2 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{5}{2} e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{5}{2} e^{2 x}

y^{^{''}} - 5 y^{^{'}} + 4 y = (12 x - 5) e^{4 x}

y^{^{''}} - 2 y^{^{'}} + y = sin (x)

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

y^{^{''}} - y = tan (x)

y^{^{''}} + y = 6 x sin (x)

What is the solution for y^{''}+3y^'+2y=30e^{2x} ?
The solution for y^{''}+3y^'+2y=30e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+5/2 e^{2x}