What is the solution for y^{''}+6y^'-16y=-272sin(8x) ?

The solution for y^{''}+6y^'-16y=-272sin(8x) is y=c_{1}e^{2x}+c_{2}e^{-8x}+5/2 sin(8x)+3/2 cos(8x)

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y^{''}+6y^'-16y=-272sin(8x)

y^{^{''}} + 6 y^{^{'}} - 16 y = - 272 sin (8 x)

y = c_{1} e^{2 x} + c_{2} e^{- 8 x} + \frac{5}{2} sin (8 x) + \frac{3}{2} cos (8 x)

Solution steps

y^{''} (x) + 6 y^{'} (x) - 16 y = - 272 sin (8 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 8 x} + \frac{5}{2} sin (8 x) + \frac{3}{2} cos (8 x)

y = c_{1} e^{2 x} + c_{2} e^{- 8 x} + \frac{5}{2} sin (8 x) + \frac{3}{2} cos (8 x)

\frac{d}{d x} (\frac{ln ( cos ( 2 x ) )}{x})

\frac{d}{d x} (2 x e^{- 4 x})

y = sin (3 x) + cos (8 x)

\frac{d}{d x} (cos (3 x))

\frac{d}{d x} (arcsin (x) + arccos (x))

What is the solution for y^{''}+6y^'-16y=-272sin(8x) ?
The solution for y^{''}+6y^'-16y=-272sin(8x) is y=c_{1}e^{2x}+c_{2}e^{-8x}+5/2 sin(8x)+3/2 cos(8x)