What is the solution for y^{''}+25y=-50sin(5t) ?

The solution for y^{''}+25y=-50sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+5tcos(5t)

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y^{''}+25y=-50sin(5t)

y^{^{''}} + 25 y = - 50 sin (5 t)

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

Solution steps

y^{''} (t) + 25 y = - 50 sin (5 t)

Solve linear ODE:

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

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

\frac{d}{d x} (1 - (1 + \frac{x}{200}) e^{- \frac{x}{200}})

\int_{0}^{3 π} sin (x) d x

\frac{1}{5 + 7 x}

\int \frac{cos ^{2} ( x )}{4 + sin ( 2 x )} d x

\frac{d}{d x} (2 x^{3} - 9 x^{2} + 12 x)

What is the solution for y^{''}+25y=-50sin(5t) ?
The solution for y^{''}+25y=-50sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+5tcos(5t)