What is the solution for (d^2-6d+13)y=0 ?

The solution for (d^2-6d+13)y=0 is y=e^{3x}(c_{1}cos(2x)+c_{2}sin(2x))

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(d^2-6d+13)y=0

(d^{2} - 6 d + 13) y = 0

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

Solution steps

(d^{2} - 6 d + 13) y = 0

Solve linear ODE:

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

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

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

y^{^{'''}} + 12 y^{^{''}} + 36 y^{^{'}} = 0

(d^{2} + 1)^{3} y = 0

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

y^{^{'''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 0

What is the solution for (d^2-6d+13)y=0 ?
The solution for (d^2-6d+13)y=0 is y=e^{3x}(c_{1}cos(2x)+c_{2}sin(2x))