What is the solution for (d^3-d^2+2d-d)y=0 ?

The solution for (d^3-d^2+2d-d)y=0 is y=c_{1}+e^{x/2}(c_{2}cos((sqrt(3)x)/2)+c_{3}sin((sqrt(3)x)/2))

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 0

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

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

(d^{3} - 2 d^{2} - 5 d + 6) y = 0

y^{^{''}} + y^{^{'}} + 25 y = 0

What is the solution for (d^3-d^2+2d-d)y=0 ?
The solution for (d^3-d^2+2d-d)y=0 is y=c_{1}+e^{x/2}(c_{2}cos((sqrt(3)x)/2)+c_{3}sin((sqrt(3)x)/2))