What is the solution for y^{'''}+y^'=0,y(0)=0,y^'(0)=1,y^{''}(0)=2 ?

The solution for y^{'''}+y^'=0,y(0)=0,y^'(0)=1,y^{''}(0)=2 is y=2-2cos(t)+sin(t)

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

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

y = 2 - 2 cos (t) + sin (t)

Solution steps

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

Solve linear ODE:

y = 2 - 2 cos (t) + sin (t)

y = 2 - 2 cos (t) + sin (t)

y^{^{''}} + 4 y^{^{'}} + 2 y = 0

y^{^{''''}} - 8 y^{^{'''}} + 16 y^{^{''}} = 0

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

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 0, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{'''}+y^'=0,y(0)=0,y^'(0)=1,y^{''}(0)=2 ?
The solution for y^{'''}+y^'=0,y(0)=0,y^'(0)=1,y^{''}(0)=2 is y=2-2cos(t)+sin(t)