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

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

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

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

y = c_{1} - 2 cos (t) + sin (t)

Solution steps

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

Solve linear ODE:

y = c_{1} - 2 cos (t) + sin (t)

y = c_{1} - 2 cos (t) + sin (t)

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

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

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

y^{^{''}} - 10 y^{^{'}} - 98 y = 0

y^{^{''}} - 4 y^{^{'}} + y 5 = 0

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