What is the solution for 4y^{''}+16y=sin(x)+2cos(x) ?

The solution for 4y^{''}+16y=sin(x)+2cos(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/12 sin(x)+1/6 cos(x)

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4y^{''}+16y=sin(x)+2cos(x)

4 y^{^{''}} + 16 y = sin (x) + 2 cos (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{12} sin (x) + \frac{1}{6} cos (x)

Solution steps

4 y^{''} (x) + 16 y = sin (x) + 2 cos (x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{12} sin (x) + \frac{1}{6} cos (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{12} sin (x) + \frac{1}{6} cos (x)

What is the solution for 4y^{''}+16y=sin(x)+2cos(x) ?
The solution for 4y^{''}+16y=sin(x)+2cos(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/12 sin(x)+1/6 cos(x)