What is the solution for y^{''}+16y=8cos(4x)+12sin(4x) ?

The solution for y^{''}+16y=8cos(4x)+12sin(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)+xsin(4x)-(3xcos(4x))/2

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y^{''}+16y=8cos(4x)+12sin(4x)

y^{^{''}} + 16 y = 8 cos (4 x) + 12 sin (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + x sin (4 x) - \frac{3 x cos ( 4 x )}{2}

Solution steps

y^{''} (x) + 16 y = 8 cos (4 x) + 12 sin (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + x sin (4 x) - \frac{3 x cos ( 4 x )}{2}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + x sin (4 x) - \frac{3 x cos ( 4 x )}{2}

\frac{d ^{2} x}{d t ^{2}} + 9 x = 5 sin (3 t)

y^{^{''}} - y^{^{'}} - 2 y = (6 x^{2} + 8 x + 7) e^{x}

y^{^{''}} - 2 y^{^{'}} - 3 y = (3 x^{2} - 5) e^{- x}

2 y^{^{''}} - 8 y = 16 e^{x}

(d^{3} - 3 d - 2) y = 540 x^{3} e^{- x}

What is the solution for y^{''}+16y=8cos(4x)+12sin(4x) ?
The solution for y^{''}+16y=8cos(4x)+12sin(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)+xsin(4x)-(3xcos(4x))/2