What is the solution for y^{''}-25y=3x^2-2+e^x ?

The solution for y^{''}-25y=3x^2-2+e^x is y=c_{1}e^{5x}+c_{2}e^{-5x}-(3x^2)/(25)+44/625-1/24 e^x

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y^{''}-25y=3x^2-2+e^x

y^{^{''}} - 25 y = 3 x^{2} - 2 + e^{x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{3 x ^{2}}{25} + \frac{44}{625} - \frac{1}{24} e^{x}

Solution steps

y^{''} (x) - 25 y = 3 x^{2} - 2 + e^{x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{3 x ^{2}}{25} + \frac{44}{625} - \frac{1}{24} e^{x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{3 x ^{2}}{25} + \frac{44}{625} - \frac{1}{24} e^{x}

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 12

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

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

What is the solution for y^{''}-25y=3x^2-2+e^x ?
The solution for y^{''}-25y=3x^2-2+e^x is y=c_{1}e^{5x}+c_{2}e^{-5x}-(3x^2)/(25)+44/625-1/24 e^x