What is the solution for y^{'''}-y^'=0,y(0)=4,y^'(0)=0,y^{''}(0)=9 ?

The solution for y^{'''}-y^'=0,y(0)=4,y^'(0)=0,y^{''}(0)=9 is y= 9/2 e^{-t}+9/2 e^t-5

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y^{'''}-y^'=0,y(0)=4,y^'(0)=0,y^{''}(0)=9

y^{^{'''}} - y^{^{'}} = 0, y (0) = 4, y^{^{'}} (0) = 0, y^{^{''}} (0) = 9

y = \frac{9}{2} e^{- t} + \frac{9}{2} e^{t} - 5

Solution steps

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

Solve linear ODE:

y = \frac{9}{2} e^{- t} + \frac{9}{2} e^{t} - 5

y = \frac{9}{2} e^{- t} + \frac{9}{2} e^{t} - 5

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 8

4 y^{^{'''}} + 4 y^{^{''}} + y^{^{'}} = 0

y^{^{'''}} - 2 y^{^{''}} - 7 y^{^{'}} - 4 y = 0

y^{^{''}} - 5 y + 2 y = 0

y^{^{''}} - y = 0, y (0) = 5, y^{^{'}} (0) = 1

What is the solution for y^{'''}-y^'=0,y(0)=4,y^'(0)=0,y^{''}(0)=9 ?
The solution for y^{'''}-y^'=0,y(0)=4,y^'(0)=0,y^{''}(0)=9 is y= 9/2 e^{-t}+9/2 e^t-5