What is the solution for y^{''}-y^'-2y=-8t+6t^2 ?

The solution for y^{''}-y^'-2y=-8t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+7t-13/2

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y^{''}-y^'-2y=-8t+6t^2

y^{^{''}} - y^{^{'}} - 2 y = - 8 t + 6 t^{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 7 t - \frac{13}{2}

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = - 8 t + 6 t^{2}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 7 t - \frac{13}{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 7 t - \frac{13}{2}

x \to 2 - lim (\frac{3 x + 5}{x - 2})

\int \frac{2 t}{1 + t ^{2}} d t

y = - 2 x^{2} + 20, y = 3 x - 15

f (x) = x^{7} - 1 (x)

\int r 2 - r^{2} d r

What is the solution for y^{''}-y^'-2y=-8t+6t^2 ?
The solution for y^{''}-y^'-2y=-8t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+7t-13/2