What is the solution for y^{''}-4y^'+4y=12te^{2t}(t+1) ?

The solution for y^{''}-4y^'+4y=12te^{2t}(t+1) is y=c_{1}e^{2t}+c_{2}te^{2t}+e^{2t}t^4+2e^{2t}t^3

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y^{''}-4y^'+4y=12te^{2t}(t+1)

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 t e^{2 t} (t + 1)

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

Solution steps

y^{''} (t) - 4 y^{'} (t) + 4 y = 12 t e^{2 t} (t + 1)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 e^{4 x}, y (0) = 0, y^{^{'}} (0) = 1

(d^{2} + 4) y = cos (2 x)

y^{^{''}} - 14 y^{^{'}} + 49 y = 21 x + 2

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + 3 e^{- x}

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

What is the solution for y^{''}-4y^'+4y=12te^{2t}(t+1) ?
The solution for y^{''}-4y^'+4y=12te^{2t}(t+1) is y=c_{1}e^{2t}+c_{2}te^{2t}+e^{2t}t^4+2e^{2t}t^3