What is the solution for x^{''}+16x=2sin(t) ?

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

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x^{''}+16x=2sin(t)

x^{^{''}} + 16 x = 2 sin (t)

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

Solution steps

x^{''} (t) + 16 x = 2 sin (t)

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 5 y = 9 e^{2 x}

y^{^{'''}} + y^{^{'}} = - 2 sin (t)

y^{^{'''}} - 7 y^{^{'}} - 6 y = 26 e^{2 x}

(d^{3} - 3 d^{2} + 4) y = e^{2 x}

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

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