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

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

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

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

y = - t + e^{t} + 1

Solution steps

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

Solve linear ODE:

y = - t + e^{t} + 1

y = - t + e^{t} + 1

16 y^{^{''}} - 24 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{^{'''}} - 3 y^{^{'}} + 2 y = 0

3 y^{^{''}} - 5 y^{^{'}} - 12 y = 0

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

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

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