What is the solution for y^{''}+25y=-10sin(5t) ?

The solution for y^{''}+25y=-10sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+tcos(5t)

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y^{''}+25y=-10sin(5t)

y^{^{''}} + 25 y = - 10 sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + t cos (5 t)

Solution steps

y^{''} (t) + 25 y = - 10 sin (5 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + t cos (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + t cos (5 t)

x \to a + 1 lim (x^{2} - 1)

\frac{d}{d y} (\frac{1}{x ^{2} + y ^{2}})

\frac{d}{d x} (1 - 4 x^{2})

\int 64 - t^{2} d t

\frac{d}{d x} (- 6 e^{- x})

What is the solution for y^{''}+25y=-10sin(5t) ?
The solution for y^{''}+25y=-10sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+tcos(5t)