What is the solution for y^{''}-4y^'+4y=16-4t-6te^{2t} ?

The solution for y^{''}-4y^'+4y=16-4t-6te^{2t} is y=c_{1}e^{2t}+c_{2}te^{2t}-t+3-e^{2t}t^3

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y^{''}-4y^'+4y=16-4t-6te^{2t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 16 - 4 t - 6 t e^{2 t}

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

Solution steps

y^{''} (t) - 4 y^{'} (t) + 4 y = 16 - 4 t - 6 t e^{2 t}

Solve linear ODE:

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

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

x \to 5 lim (- 4)

\int x 4^{x^{2}} d x

\frac{d}{d t} (t e^{t})

g (t) = \frac{3 t ^{2} - 1}{2 t + 5}

\int 33 arctan (x) d x

What is the solution for y^{''}-4y^'+4y=16-4t-6te^{2t} ?
The solution for y^{''}-4y^'+4y=16-4t-6te^{2t} is y=c_{1}e^{2t}+c_{2}te^{2t}-t+3-e^{2t}t^3