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

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

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y^{''}-2y^'+y=2t-1-(6te^t+6e^t)

y^{^{''}} - 2 y^{^{'}} + y = 2 t - 1 - (6 t e^{t} + 6 e^{t})

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

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = 2 t - 1 - (6 t e^{t} + 6 e^{t})

Solve linear ODE:

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

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

1 + T^{2}

\frac{d}{d x} (\frac{4 x - 3}{x ^{2} - 2 x})

f (x) = tan^{7} (x)

e^{x} + \frac{1}{1 + x}, 0

\int 19 tan^{3} (θ) d θ

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