What is the solution for y^{'''}-8y^{''}+37y^'-50y=0 ?

The solution for y^{'''}-8y^{''}+37y^'-50y=0 is y=c_{1}e^{2t}+e^{3t}(c_{2}cos(4t)+c_{3}sin(4t))

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y^{'''}-8y^{''}+37y^'-50y=0

y^{^{'''}} - 8 y^{^{''}} + 37 y^{^{'}} - 50 y = 0

y = c_{1} e^{2 t} + e^{3 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

Solution steps

y^{'''} (t) - 8 y^{''} (t) + 37 y^{'} (t) - 50 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + e^{3 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

y = c_{1} e^{2 t} + e^{3 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

(d^{2} - 4) y = 0

(d^{3} - 9 d) \cdot y = 0

y^{^{'''}} - 9 y^{^{'}} = 0

(d^{4} - 7 d^{3} + 18 d^{2} - 20 d + 8) y = 0

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

What is the solution for y^{'''}-8y^{''}+37y^'-50y=0 ?
The solution for y^{'''}-8y^{''}+37y^'-50y=0 is y=c_{1}e^{2t}+e^{3t}(c_{2}cos(4t)+c_{3}sin(4t))