What is the solution for y^{''}-4y^'+4y=1-4e^t ?

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

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y^{''}-4y^'+4y=1-4e^t

y^{^{''}} - 4 y^{^{'}} + 4 y = 1 - 4 e^{t}

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

Solution steps

y^{''} (t) - 4 y^{'} (t) + 4 y = 1 - 4 e^{t}

Solve linear ODE:

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

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

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