What is the solution for y^{''}-7y^'+6y=sin(x) ?

The solution for y^{''}-7y^'+6y=sin(x) is y=c_{1}e^{6x}+c_{2}e^x+5/74 sin(x)+7/74 cos(x)

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y^{''}-7y^'+6y=sin(x)

y^{^{''}} - 7 y^{^{'}} + 6 y = sin (x)

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

Solution steps

y^{''} (x) - 7 y^{'} (x) + 6 y = sin (x)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{5}{74} sin (x) + \frac{7}{74} cos (x)

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

y^{^{''}} + 7 y^{^{'}} + 6 y = 8

y^{^{''}} + 4 y = 3 sin (t), y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} - 4 y = 3 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = t e^{- 2 t}

What is the solution for y^{''}-7y^'+6y=sin(x) ?
The solution for y^{''}-7y^'+6y=sin(x) is y=c_{1}e^{6x}+c_{2}e^x+5/74 sin(x)+7/74 cos(x)