What is the solution for 5y^{''}+180y=90sin(6t) ?

The solution for 5y^{''}+180y=90sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-(3tcos(6t))/2

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5y^{''}+180y=90sin(6t)

5 y^{^{''}} + 180 y = 90 sin (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{3 t cos ( 6 t )}{2}

Solution steps

5 y^{''} (t) + 180 y = 90 sin (6 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{3 t cos ( 6 t )}{2}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{3 t cos ( 6 t )}{2}

y^{^{''}} + 2 y^{^{'}} - 2 y = 8 e^{- 3 x}

y^{^{''}} + 9 y = x^{2} sin (4 x)

y^{^{''}} - y^{^{'}} - 6 y = 12 x - e^{x}, y (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x

\frac{d ^{2} y}{d x ^{2}} + y = sec (x) tan (x)

What is the solution for 5y^{''}+180y=90sin(6t) ?
The solution for 5y^{''}+180y=90sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-(3tcos(6t))/2