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

The solution for y^{''}-y^'-2y=-2t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+4t-5

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

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

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 4 t - 5

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 4 t - 5

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 4 t - 5

\frac{d}{d x} (e^{s i n^{2} (x)})

y = \frac{2}{x}, y = 8 x, y = \frac{1}{2} x

\frac{d}{d x} (\frac{3}{4 ( 2 x - 5 ) ^{8}})

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

\int ln (x) e^{- x} d x

What is the solution for y^{''}-y^'-2y=-2t+6t^2 ?
The solution for y^{''}-y^'-2y=-2t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+4t-5