What is the solution for x^{''}+2x=2t+26 ?

The solution for x^{''}+2x=2t+26 is x=c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)+t+13

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x^{''}+2x=2t+26

x^{^{''}} + 2 x = 2 t + 26

x = c_{1} cos (2 t) + c_{2} sin (2 t) + t + 13

Solution steps

x^{''} (t) + 2 x = 2 t + 26

Solve linear ODE:

x = c_{1} cos (2 t) + c_{2} sin (2 t) + t + 13

x = c_{1} cos (2 t) + c_{2} sin (2 t) + t + 13

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

y^{^{''}} - 14 y^{^{'}} + 49 y = e^{7 t} ln (t)

y^{^{''}} + 2 y = \frac{1}{cos ( 2 x )}

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

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

What is the solution for x^{''}+2x=2t+26 ?
The solution for x^{''}+2x=2t+26 is x=c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)+t+13