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

The solution for -x^{''}+x^'=6e^t+2t-2 is x=c_{1}+c_{2}e^t-6te^t+t^2

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-x^{''}+x^'=6e^t+2t-2

- x^{^{''}} + x^{^{'}} = 6 e^{t} + 2 t - 2

x = c_{1} + c_{2} e^{t} - 6 t e^{t} + t^{2}

Solution steps

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

Solve linear ODE:

x = c_{1} + c_{2} e^{t} - 6 t e^{t} + t^{2}

x = c_{1} + c_{2} e^{t} - 6 t e^{t} + t^{2}

y^{^{''}} + 5 y^{^{'}} + 6 y = 12 e^{- 5 t} + 12 e^{- t} + 24

\frac{d ^{2} y}{d x ^{2}} - y = cos (2 x)

y^{^{''}} - 2 y^{^{'}} + y = x^{3}

x^{^{''}} + 3 x^{^{'}} + 21 x = 11 cos (4 t)

y^{^{'''}} + y^{^{''}} = 2 x + 5

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