What is the solution for x^{''}+7x^'+6x=sin(2t) ?

The solution for x^{''}+7x^'+6x=sin(2t) is x=c_{1}e^{-t}+c_{2}e^{-6t}+1/100 sin(2t)-7/100 cos(2t)

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x^{''}+7x^'+6x=sin(2t)

x^{^{''}} + 7 x^{^{'}} + 6 x = sin (2 t)

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

Solution steps

x^{''} (t) + 7 x^{'} (t) + 6 x = sin (2 t)

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

y^{^{''}} - 25 y = e^{5 x}

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

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

y^{^{''}} + 4 y = t^{2} + 3 e t, y (0) = 0, y^{^{'}} (0) = 2

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

What is the solution for x^{''}+7x^'+6x=sin(2t) ?
The solution for x^{''}+7x^'+6x=sin(2t) is x=c_{1}e^{-t}+c_{2}e^{-6t}+1/100 sin(2t)-7/100 cos(2t)