What is the solution for 3y^{''}+75y=10cos(5t) ?

The solution for 3y^{''}+75y=10cos(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+(tsin(5t))/3

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3y^{''}+75y=10cos(5t)

3 y^{^{''}} + 75 y = 10 cos (5 t)

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

Solution steps

3 y^{''} (t) + 75 y = 10 cos (5 t)

Solve linear ODE:

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

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

y^{^{''''}} - y = 8 e^{x}

(D^{2} + 9) y = cos (2 x)

y^{^{''}} + y = t, y (0) = 4, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 2 y = 2 t^{2} + 4 t + 4

y^{^{''}} + 4 y^{^{'}} + 4 y = t^{2} - 2 t

What is the solution for 3y^{''}+75y=10cos(5t) ?
The solution for 3y^{''}+75y=10cos(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)+(tsin(5t))/3