What is the solution for y^{''}+2y^'-3y=4e^{-3x}+10sin(x) ?

The solution for y^{''}+2y^'-3y=4e^{-3x}+10sin(x) is y=c_{1}e^x+c_{2}e^{-3x}-e^{-3x}x-2sin(x)-cos(x)

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y^{''}+2y^'-3y=4e^{-3x}+10sin(x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{- 3 x} + 10 sin (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - e^{- 3 x} x - 2 sin (x) - cos (x)

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 4 e^{- 3 x} + 10 sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} - e^{- 3 x} x - 2 sin (x) - cos (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - e^{- 3 x} x - 2 sin (x) - cos (x)

What is the solution for y^{''}+2y^'-3y=4e^{-3x}+10sin(x) ?
The solution for y^{''}+2y^'-3y=4e^{-3x}+10sin(x) is y=c_{1}e^x+c_{2}e^{-3x}-e^{-3x}x-2sin(x)-cos(x)