What is the solution for y^{''}-7y^'+12y=sin(x)-cos(x) ?

The solution for y^{''}-7y^'+12y=sin(x)-cos(x) is y=c_{1}e^{4x}+c_{2}e^{3x}+9/85 sin(x)-2/85 cos(x)

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y^{''}-7y^'+12y=sin(x)-cos(x)

y^{^{''}} - 7 y^{^{'}} + 12 y = sin (x) - cos (x)

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{9}{85} sin (x) - \frac{2}{85} cos (x)

Solution steps

y^{''} (x) - 7 y^{'} (x) + 12 y = sin (x) - cos (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{9}{85} sin (x) - \frac{2}{85} cos (x)

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{9}{85} sin (x) - \frac{2}{85} cos (x)

What is the solution for y^{''}-7y^'+12y=sin(x)-cos(x) ?
The solution for y^{''}-7y^'+12y=sin(x)-cos(x) is y=c_{1}e^{4x}+c_{2}e^{3x}+9/85 sin(x)-2/85 cos(x)