I Second order ordinary differential equation to a system of first order

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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
IMG_20180525_211314.jpg
differs from the book?. I've attached both the book solution and mine. Thanks.
 

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tnich

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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

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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 ?
 
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Thanks very much
 

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