What is the solution for (d^2-3d+2)*y=3sin(x) ?

The solution for (d^2-3d+2)*y=3sin(x) is y=c_{1}e^{2x}+c_{2}e^x+3/10 sin(x)+9/10 cos(x)

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(d^2-3d+2)*y=3sin(x)

(d^{2} - 3 d + 2) \cdot y = 3 sin (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{3}{10} sin (x) + \frac{9}{10} cos (x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{3}{10} sin (x) + \frac{9}{10} cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{3}{10} sin (x) + \frac{9}{10} cos (x)

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

y^{^{'''}} - 4 y^{^{'}} = 0

y^{^{'''}} - 4 y = 0

2 y^{^{''}} - 3 y^{^{'}} + y = 0, y (0) = 0, y^{^{'}} (0) = 1

(d^{2} - 3 d + 2) y = 0

What is the solution for (d^2-3d+2)*y=3sin(x) ?
The solution for (d^2-3d+2)*y=3sin(x) is y=c_{1}e^{2x}+c_{2}e^x+3/10 sin(x)+9/10 cos(x)