What is the solution for y^{''}-3y^'+2y=4e^{2t} ?

The solution for y^{''}-3y^'+2y=4e^{2t} is y=c_{1}e^{2t}+c_{2}e^t+4te^{2t}

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y^{''}-3y^'+2y=4e^{2t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + 4 t e^{2 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = 4 e^{2 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + 4 t e^{2 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + 4 t e^{2 t}

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\frac{\partial}{\partial x} (3 e^{x y + 4})

\frac{d y}{d x} = x y + 5 x + 2 y + 10

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What is the solution for y^{''}-3y^'+2y=4e^{2t} ?
The solution for y^{''}-3y^'+2y=4e^{2t} is y=c_{1}e^{2t}+c_{2}e^t+4te^{2t}