What is the solution for 1/16 x^{''}+x=10sin(4t) ?

The solution for 1/16 x^{''}+x=10sin(4t) is x=c_{1}cos(4t)+c_{2}sin(4t)-20tcos(4t)

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1/16 x^{''}+x=10sin(4t)

\frac{1}{16} x^{^{''}} + x = 10 sin (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 20 t cos (4 t)

Solution steps

\frac{1}{16} x^{''} (t) + x = 10 sin (4 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 20 t cos (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 20 t cos (4 t)

What is the solution for 1/16 x^{''}+x=10sin(4t) ?
The solution for 1/16 x^{''}+x=10sin(4t) is x=c_{1}cos(4t)+c_{2}sin(4t)-20tcos(4t)