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

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

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y^{''}-2y^'+y=12te^t+2e^t+t-4

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (8 x - 2 x^{2})

\frac{x ^{2}}{2}

f (x) = (x + 8)^{3 x}

sin^{2} (x), sin^{4} (x)

x \to - 6 lim (36 - x^{2})

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