What is the solution for y''-25y=x^2+x ?

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

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y''-25y=x^2+x

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

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

Solution steps

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

Solve linear ODE:

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

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

D, D (x) = \frac{45}{x + 3}

y^{^{''}} - y^{^{'}} = t

y^{^{''}} + y = x^{2} + x - 1

y^{^{''}} + 4 y^{^{'}} + 5 y = 1

(D^{3} - 3 D^{2} + 4 D - 2) y = cos (x)

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