What is the solution for y^{''}+9y=tsin(5t) ?

The solution for y^{''}+9y=tsin(5t) is y=c_{1}cos(3t)+c_{2}sin(3t)-(tsin(5t))/(16)-5/128 cos(5t)

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y^{''}+9y=tsin(5t)

y^{^{''}} + 9 y = t sin (5 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{t sin ( 5 t )}{16} - \frac{5}{128} cos (5 t)

Solution steps

y^{''} (t) + 9 y = t sin (5 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{t sin ( 5 t )}{16} - \frac{5}{128} cos (5 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{t sin ( 5 t )}{16} - \frac{5}{128} cos (5 t)

\frac{d}{d x} (5 5 x - 4)

\int 5 e^{2 x + e^{2 x}} d x

\int x^{2} + y^{2} d x

x \to 5 lim (\frac{1}{x})

\frac{d}{d x} (1 + sin (x))

What is the solution for y^{''}+9y=tsin(5t) ?
The solution for y^{''}+9y=tsin(5t) is y=c_{1}cos(3t)+c_{2}sin(3t)-(tsin(5t))/(16)-5/128 cos(5t)