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

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

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

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

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{25} - \frac{2}{625}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{25} - \frac{2}{625}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{25} - \frac{2}{625}

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

5 y^{^{''}} + 6 y^{^{'}} + \frac{5}{1.96} y = 3 cos (2 t)

y^{^{''}} + 200 y^{^{'}} + 1000000 = 0

f^{^{''}} (t) + f (t) = cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 4 t}, y (0) = 1

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