What is the solution for y^{''}+9y=2e^{3t}+2cos(2t) ?

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

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y^{''}+9y=2e^{3t}+2cos(2t)

y^{^{''}} + 9 y = 2 e^{3 t} + 2 cos (2 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{9} e^{3 t} + \frac{2}{5} cos (2 t)

Solution steps

y^{''} (t) + 9 y = 2 e^{3 t} + 2 cos (2 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{9} e^{3 t} + \frac{2}{5} cos (2 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{9} e^{3 t} + \frac{2}{5} cos (2 t)

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