What is the solution for y^{'''}+4y^{''}-35y^'-150y=0 ?

The solution for y^{'''}+4y^{''}-35y^'-150y=0 is y=c_{1}e^{6t}+c_{2}e^{-5t}+c_{3}te^{-5t}

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y^{'''}+4y^{''}-35y^'-150y=0

y^{^{'''}} + 4 y^{^{''}} - 35 y^{^{'}} - 150 y = 0

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

Solution steps

y^{'''} (t) + 4 y^{''} (t) - 35 y^{'} (t) - 150 y = 0

Solve linear ODE:

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

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

\int \frac{1}{x ^{\frac{1}{3}} ( x ^{\frac{2}{3}} + 4 )} d x

\frac{d}{d x} (cos^{2} (x^{2}))

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

(6.3) (4.2)

\int t^{2} - 1 d t

What is the solution for y^{'''}+4y^{''}-35y^'-150y=0 ?
The solution for y^{'''}+4y^{''}-35y^'-150y=0 is y=c_{1}e^{6t}+c_{2}e^{-5t}+c_{3}te^{-5t}