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)

y^{^{''}} - 12 y^{^{'}} + 36 y = 12 x + 6

y^{^{''}} - 12 y^{^{'}} + 36 y = 36 x + 2

x^{^{''}} + 100 x^{^{'}} + 2500 x = 30

16 y^{^{''}} + 24 y^{^{'}} + 9 = 0

(D^{3} + D^{2} - 4 D - 4) y = 3 e^{- x} - 4 x - 6

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)