What is the solution for y^{''}+750/30 y= 20/30 cos(2)t ?

The solution for y^{''}+750/30 y= 20/30 cos(2)t is y=c_{1}cos(5t)+c_{2}sin(5t)+(2cos(2)t)/(75)

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y^{''}+750/30 y= 20/30 cos(2)t

y^{^{''}} + \frac{750}{30} y = \frac{20}{30} cos (2) t

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{2 cos ( 2 ) t}{75}

Solution steps

y^{''} (t) + \frac{750}{30} y = \frac{20}{30} cos (2) t

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{2 cos ( 2 ) t}{75}

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{2 cos ( 2 ) t}{75}

5 y^{^{''}} + 180 y = 150 sin (3 t)

y^{^{''}} - 2 y^{^{'}} + y = e^{2 x} (e^{x} + 1)^{- 2}

y^{^{''}} + 25 y = cos (9 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 t}}{e ^{2 t} + 1}

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

What is the solution for y^{''}+750/30 y= 20/30 cos(2)t ?
The solution for y^{''}+750/30 y= 20/30 cos(2)t is y=c_{1}cos(5t)+c_{2}sin(5t)+(2cos(2)t)/(75)