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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + \frac{1}{2} y = 0

y^{^{''}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 6

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\frac{3 y ^{^{''}} + 2 y ^{^{'}} + y}{4} = 0

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

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