What is the solution for 2y^{''}+6y^'-20y=2x-3 ?

The solution for 2y^{''}+6y^'-20y=2x-3 is y=c_{1}e^{2x}+c_{2}e^{-5x}-x/(10)+3/25

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2y^{''}+6y^'-20y=2x-3

2 y^{^{''}} + 6 y^{^{'}} - 20 y = 2 x - 3

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - \frac{x}{10} + \frac{3}{25}

Solution steps

2 y^{''} (x) + 6 y^{'} (x) - 20 y = 2 x - 3

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - \frac{x}{10} + \frac{3}{25}

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - \frac{x}{10} + \frac{3}{25}

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

y^{^{''}} - 4 y^{^{'}} - 32 y = 108 e^{2 t}

y^{^{''}} + 16 y = 32 sec (2 x)

y^{^{''''}} - y^{^{'''}} - y^{^{''}} - y^{^{'}} - 2 y = 8 x^{5}

(d^{2} - 2 d + 5) y = e^{x}

What is the solution for 2y^{''}+6y^'-20y=2x-3 ?
The solution for 2y^{''}+6y^'-20y=2x-3 is y=c_{1}e^{2x}+c_{2}e^{-5x}-x/(10)+3/25