What is the solution for y^{''}+25y=-30sin(5t) ?

The solution for y^{''}+25y=-30sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+3tcos(5t)

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y^{''}+25y=-30sin(5t)

y^{^{''}} + 25 y = - 30 sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + 3 t cos (5 t)

Solution steps

y^{''} (t) + 25 y = - 30 sin (5 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + 3 t cos (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + 3 t cos (5 t)

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

\frac{d}{d x} (2 (1 + cos (x)))

\frac{d}{d x} (\frac{1 - e ^{7 x}}{1 + e ^{7 x}})

y = x^{\frac{8}{5}}

x \to 1 lim (e^{5 x^{5} - 5 x})

What is the solution for y^{''}+25y=-30sin(5t) ?
The solution for y^{''}+25y=-30sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+3tcos(5t)