What is the solution for y^{''}+9y^'=18e^xsin(x) ?

The solution for y^{''}+9y^'=18e^xsin(x) is y=c_{1}+c_{2}e^{-9x}+81/101 e^xsin(x)-99/101 e^xcos(x)

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y^{''}+9y^'=18e^xsin(x)

y^{^{''}} + 9 y^{^{'}} = 18 e^{x} sin (x)

y = c_{1} + c_{2} e^{- 9 x} + \frac{81}{101} e^{x} sin (x) - \frac{99}{101} e^{x} cos (x)

Solution steps

y^{''} (x) + 9 y^{'} (x) = 18 e^{x} sin (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 9 x} + \frac{81}{101} e^{x} sin (x) - \frac{99}{101} e^{x} cos (x)

y = c_{1} + c_{2} e^{- 9 x} + \frac{81}{101} e^{x} sin (x) - \frac{99}{101} e^{x} cos (x)

y^{^{''}} + 4 y = 3 cos (t)

y^{^{''}} + 3 y^{^{'}} + 1 = 0

4 y^{^{''}} - y = \frac{e x}{2 + 4}

y^{^{''}} - 10 y^{^{'}} + 25 y = (\frac{e ^{- 5 x}}{1 + x ^{2}})

x^{^{''}} - 12 x^{^{'}} + 36 x = 2 t + e^{6 t}

What is the solution for y^{''}+9y^'=18e^xsin(x) ?
The solution for y^{''}+9y^'=18e^xsin(x) is y=c_{1}+c_{2}e^{-9x}+81/101 e^xsin(x)-99/101 e^xcos(x)