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

The solution for x^{''}+16x=sin(t) is x=c_{1}cos(4t)+c_{2}sin(4t)+1/15 sin(t)

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x^{''}+16x=sin(t)

x^{^{''}} + 16 x = sin (t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{15} sin (t)

Solution steps

x^{''} (t) + 16 x = sin (t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{15} sin (t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{15} sin (t)

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} - 20 y = 5 e^{- 3 t}

y^{^{''}} + y^{^{'}} + 4 = - 20 x

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 3

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 2

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 15 = 0

What is the solution for x^{''}+16x=sin(t) ?
The solution for x^{''}+16x=sin(t) is x=c_{1}cos(4t)+c_{2}sin(4t)+1/15 sin(t)