What is the solution for 144y^{'''}+168y^{''}+49y^'=0 ?

The solution for 144y^{'''}+168y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-(7t)/(12)}+c_{3}e^{-(7t)/(12)}t

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144y^{'''}+168y^{''}+49y^'=0

144 y^{^{'''}} + 168 y^{^{''}} + 49 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{7 t}{12}} + c_{3} e^{- \frac{7 t}{12}} t

Solution steps

144 y^{'''} (t) + 168 y^{''} (t) + 49 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{7 t}{12}} + c_{3} e^{- \frac{7 t}{12}} t

y = c_{1} + c_{2} e^{- \frac{7 t}{12}} + c_{3} e^{- \frac{7 t}{12}} t

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

x \frac{d y}{d x} = y + x e^{x}

\frac{d}{d x} (\frac{3}{x + 5})

\int 19 tan^{3} (x) d x

\int (1 - cos (θ))^{3} d θ

What is the solution for 144y^{'''}+168y^{''}+49y^'=0 ?
The solution for 144y^{'''}+168y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-(7t)/(12)}+c_{3}e^{-(7t)/(12)}t