What is the solution for x^{'''}-x^{''}=0,x(0)=1,x^'(0)=3,x^{''}(0)=2 ?

The solution for x^{'''}-x^{''}=0,x(0)=1,x^'(0)=3,x^{''}(0)=2 is x=t+2e^t-1

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x^{'''}-x^{''}=0,x(0)=1,x^'(0)=3,x^{''}(0)=2

x^{^{'''}} - x^{^{''}} = 0, x (0) = 1, x^{^{'}} (0) = 3, x^{^{''}} (0) = 2

x = t + 2 e^{t} - 1

Solution steps

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

Solve linear ODE:

x = t + 2 e^{t} - 1

x = t + 2 e^{t} - 1

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