What is the solution for y^{''}-5y^'+4y=e^{2t} ?

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

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y^{''}-5y^'+4y=e^{2t}

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{2 t}

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

Solution steps

y^{''} (t) - 5 y^{'} (t) + 4 y = e^{2 t}

Solve linear ODE:

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

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

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