What is the solution for y^{''}-6y^'+8y=85sin(x) ?

The solution for y^{''}-6y^'+8y=85sin(x) is y=c_{1}e^{4x}+c_{2}e^{2x}+7sin(x)+6cos(x)

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y^{''}-6y^'+8y=85sin(x)

y^{^{''}} - 6 y^{^{'}} + 8 y = 85 sin (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 7 sin (x) + 6 cos (x)

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = 85 sin (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 7 sin (x) + 6 cos (x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 7 sin (x) + 6 cos (x)

x^{^{''}} + 9 x = 2 (t - 1) \cdot 2 (t - 2), x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 10 x + 3

\frac{d q}{20 - q} = \frac{1}{16} d T

y^{^{''}} - y^{^{'}} + 4 y = 4, e^{2 x} y (0) = 2, y^{^{'}} (0) = 4

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{2 x} + 1

What is the solution for y^{''}-6y^'+8y=85sin(x) ?
The solution for y^{''}-6y^'+8y=85sin(x) is y=c_{1}e^{4x}+c_{2}e^{2x}+7sin(x)+6cos(x)