What is the solution for y^{'''}+9y^'=0,y(0)=5,y^'(0)=4,y^{''}(0)=3 ?

The solution for y^{'''}+9y^'=0,y(0)=5,y^'(0)=4,y^{''}(0)=3 is y=5+1/3-1/3 cos(3t)+4/3 sin(3t)

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y^{'''}+9y^'=0,y(0)=5,y^'(0)=4,y^{''}(0)=3

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = 5, y^{^{'}} (0) = 4, y^{^{''}} (0) = 3

y = 5 + \frac{1}{3} - \frac{1}{3} cos (3 t) + \frac{4}{3} sin (3 t)

Solution steps

y^{'''} (t) + 9 y^{'} (t) = 0

Solve linear ODE:

y = 5 + \frac{1}{3} - \frac{1}{3} cos (3 t) + \frac{4}{3} sin (3 t)

y = 5 + \frac{1}{3} - \frac{1}{3} cos (3 t) + \frac{4}{3} sin (3 t)

y^{^{''}} - \frac{2}{5} y = 0

y^{^{''''}} + 2 y^{^{'''}} - 4 y^{^{''}} - 2 y^{^{'}} + \frac{1}{2} y = 0

2.25 y^{^{''}} - 3 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = - 1

12 x^{^{''}} + 6 x^{^{'}} + 18 x = 0

b \cdot y = (a - v^{2}) y^{^{''}}

What is the solution for y^{'''}+9y^'=0,y(0)=5,y^'(0)=4,y^{''}(0)=3 ?
The solution for y^{'''}+9y^'=0,y(0)=5,y^'(0)=4,y^{''}(0)=3 is y=5+1/3-1/3 cos(3t)+4/3 sin(3t)