What is the solution for (d^2y)/(dx^2)+25y=5x^2+x ?

The solution for (d^2y)/(dx^2)+25y=5x^2+x is y=c_{1}cos(5x)+c_{2}sin(5x)+(x^2)/5+x/(25)-2/125

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(d^2y)/(dx^2)+25y=5x^2+x

\frac{d ^{2} y}{d x ^{2}} + 25 y = 5 x^{2} + x

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{5} + \frac{x}{25} - \frac{2}{125}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 25 y = 5 x^{2} + x

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{5} + \frac{x}{25} - \frac{2}{125}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x ^{2}}{5} + \frac{x}{25} - \frac{2}{125}

25 y^{^{''}} - 9 y = sin (x)

y^{^{''}} + 2 y^{^{'}} - 24 y = 6 x

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t)

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

y^{^{''}} + y = sec (x) csc (x)

What is the solution for (d^2y)/(dx^2)+25y=5x^2+x ?
The solution for (d^2y)/(dx^2)+25y=5x^2+x is y=c_{1}cos(5x)+c_{2}sin(5x)+(x^2)/5+x/(25)-2/125