Second order ordinary differential equation to a system of first order

[LSMOG]

I tried to convert the second order ordinary differential equation to a system of first order differential equations and to write it in a matrix form. I took it from the book by LM Hocking on (Optimal control). What did I do wrong in this attachment because mine

differs from the book?. I've attached both the book solution and mine. Thanks.

 

[tnich]

I tried to convert the second order ordinary differential equation to a system of first order differential equations and to write it in a matrix form. I took it from the book by LM Hocking on (Optimal control). What did I do wrong in this attachment because mineView attachment 226158 differs from the book?. I've attached both the book solution and mine. Thanks.

I don't think there is anything wrong with your way (except for the $\frac 1 k$ you have penciled in front of the matrix in your equation). It still leads to the same solution to the differential equation. Your way does require fiddling with the constants a little more to get to that solution, which may be why your textbook gives the particular form you found there.

 

[BvU]

You didn't do anything wrong. Just that your definition of $x_2$ is different from that in the book.
When I do this I do it the same way you do, but perhaps the book author has some specific reason for his approach ?

 

[LSMOG]

Thanks very much