What is the solution for y^{'''}-7y^{''}+6y=0 ?

The solution for y^{'''}-7y^{''}+6y=0 is y=c_{1}e^t+c_{2}e^{(3+sqrt(15))t}+c_{3}e^{(3-sqrt(15))t}

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y^{'''}-7y^{''}+6y=0

y^{^{'''}} - 7 y^{^{''}} + 6 y = 0

y = c_{1} e^{t} + c_{2} e^{(3 + 15) t} + c_{3} e^{(3 - 15) t}

Solution steps

y^{'''} (t) - 7 y^{''} (t) + 6 y = 0

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{(3 + 15) t} + c_{3} e^{(3 - 15) t}

y = c_{1} e^{t} + c_{2} e^{(3 + 15) t} + c_{3} e^{(3 - 15) t}

What is the solution for y^{'''}-7y^{''}+6y=0 ?
The solution for y^{'''}-7y^{''}+6y=0 is y=c_{1}e^t+c_{2}e^{(3+sqrt(15))t}+c_{3}e^{(3-sqrt(15))t}