What is the solution for y^{'''}+y^{''}-30y^'=0 ?

The solution for y^{'''}+y^{''}-30y^'=0 is y=c_{1}+c_{2}e^{5t}+c_{3}e^{-6t}

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y^{'''}+y^{''}-30y^'=0

y^{^{'''}} + y^{^{''}} - 30 y^{^{'}} = 0

y = c_{1} + c_{2} e^{5 t} + c_{3} e^{- 6 t}

Solution steps

y^{'''} (t) + y^{''} (t) - 30 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{5 t} + c_{3} e^{- 6 t}

y = c_{1} + c_{2} e^{5 t} + c_{3} e^{- 6 t}

θ^{^{''}} (t) + 16.33 θ (t) = 0

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

x^{^{''}} + \frac{1536}{25} x = 0

10 y^{^{''}} + 40 y^{^{'}} + 240 y = 0

x^{^{''}} + 2 x^{^{'}} + 3 x = 0, x (0) = 1, x^{^{'}} (0) = 0

What is the solution for y^{'''}+y^{''}-30y^'=0 ?
The solution for y^{'''}+y^{''}-30y^'=0 is y=c_{1}+c_{2}e^{5t}+c_{3}e^{-6t}