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

The solution for y^{'''}+y^'=0,y(0)=2,y^'(0)=1,y^{''}(0)=1 is y=sin(t)-cos(t)+3

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

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

y = sin (t) - cos (t) + 3

Solution steps

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

Solve linear ODE:

y = sin (t) - cos (t) + 3

y = sin (t) - cos (t) + 3

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

10 x^{^{''}} + 200 x = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = - 3

5 y^{^{''}} + 2 y^{^{'}} + 7 y = 0

3 y^{^{''}} + 8 y^{^{'}} + 3 y = 0

What is the solution for y^{'''}+y^'=0,y(0)=2,y^'(0)=1,y^{''}(0)=1 ?
The solution for y^{'''}+y^'=0,y(0)=2,y^'(0)=1,y^{''}(0)=1 is y=sin(t)-cos(t)+3