What is the solution for y^{''}-10y^'+16y=17sin(2x) ?

The solution for y^{''}-10y^'+16y=17sin(2x) is y=c_{1}e^{8x}+c_{2}e^{2x}+3/8 sin(2x)+5/8 cos(2x)

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y^{''}-10y^'+16y=17sin(2x)

y^{^{''}} - 10 y^{^{'}} + 16 y = 17 sin (2 x)

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

Solution steps

y^{''} (x) - 10 y^{'} (x) + 16 y = 17 sin (2 x)

Solve linear ODE:

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

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

What is the solution for y^{''}-10y^'+16y=17sin(2x) ?
The solution for y^{''}-10y^'+16y=17sin(2x) is y=c_{1}e^{8x}+c_{2}e^{2x}+3/8 sin(2x)+5/8 cos(2x)