What is the solution for y^{''}+25y=5t^2 ?

The solution for y^{''}+25y=5t^2 is y=c_{1}cos(5t)+c_{2}sin(5t)+(t^2)/5-2/125

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y^{''}+25y=5t^2

y^{^{''}} + 25 y = 5 t^{2}

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

Solution steps

y^{''} (t) + 25 y = 5 t^{2}

Solve linear ODE:

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

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

\frac{8}{7 x ^{9} + 3}

x \to 0 + lim (x^{7 x})

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\int \frac{( x ^{2} )}{2 ^{x}} d x

\frac{d}{d x} (2 (- 2 x^{2} sin (x^{2}) + cos (x^{2})))

What is the solution for y^{''}+25y=5t^2 ?
The solution for y^{''}+25y=5t^2 is y=c_{1}cos(5t)+c_{2}sin(5t)+(t^2)/5-2/125