What is the solution for y^{''}-6y^'+8y=3cos(x) ?

The solution for y^{''}-6y^'+8y=3cos(x) is y=c_{1}e^{4x}+c_{2}e^{2x}-18/85 sin(x)+21/85 cos(x)

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y^{''}-6y^'+8y=3cos(x)

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 cos (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = 3 cos (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{18}{85} sin (x) + \frac{21}{85} cos (x)

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

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

(d^{2} + 1) y = x^{2} e^{2} x

y^{^{''}} + y = \frac{1}{sin ( x )}

y^{^{''}} - 4 y^{^{'}} - 5 y = 4 x^{2} e^{2 x}

What is the solution for y^{''}-6y^'+8y=3cos(x) ?
The solution for y^{''}-6y^'+8y=3cos(x) is y=c_{1}e^{4x}+c_{2}e^{2x}-18/85 sin(x)+21/85 cos(x)