What is the solution for y^{''}-4y^'+4y=6t^2e^{2t} ?

The solution for y^{''}-4y^'+4y=6t^2e^{2t} is y=c_{1}e^{2t}+c_{2}te^{2t}+(e^{2t}t^4)/2

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y^{''}-4y^'+4y=6t^2e^{2t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 t^{2} e^{2 t}

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

Solution steps

y^{''} (t) - 4 y^{'} (t) + 4 y = 6 t^{2} e^{2 t}

Solve linear ODE:

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

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

What is the solution for y^{''}-4y^'+4y=6t^2e^{2t} ?
The solution for y^{''}-4y^'+4y=6t^2e^{2t} is y=c_{1}e^{2t}+c_{2}te^{2t}+(e^{2t}t^4)/2