Mathematica I have a problem with mathematica

[Reem Hashem]

Hello,I need help in Mathematica,my problem is that I wrote the system of differential equations and I put a certain value of the variables and it is supposed that the value of the absolute of the determent would be zero but unfortunately I did not get zero , I got another answer
when I put R=0,S=0,h=0,a=3.127,w=3390 the absolute will be zero
but when I put R=5,S=8.2,a=3.116,w=3426,h=0 the answer was not zero which is supposed to be zero as what is written in the research.So Is my writing of the equation in mathematica wrong?
I wrote the equations by my hand writing and also in Mathematica,so I hope to Know where is the mistake in writing the system in Mathematica?and thanks for help

 

[Bill Simpson]

I tried to see if your hand written y'[19]== and your Mathematica y'[19]== were the same and I can't get those anywhere near the same. I am guessing your translation into Mathematica has changed enough things that I cannot verify any of your more complicated equations.

 

[Reem Hashem]

Sorry Mr Bill ,but I think that you did not notice that in my hand writing I wrote that
m= (S+(h(w^0.5)+aR)(1-t) & K= a^2 w(1-t) so when you susitute them in the equations you will find that they are the same what I wrote in Mathematica

 

[Bill Simpson]

I did notice that, but the difference in notation between your handwriting and Mathematica makes it more difficult than I have the time to spend to repeat the complete translation myself to find what is perhaps a typographical error somewhere.

And there is at least as big a chance that I'll make a different typo trying to do the translation myself.

 

[Reem Hashem]

Compare between my handwriting & mathematica

Mr Bill ,thank you very much for helping me alot, I sent the new equations in my handwriting ,I hope it will better this time to compare with what I wrote in mathematica

 

[Reem Hashem]

Mr Bill I tried to find the value of (w=T) which makes the determinte =0 when R=5,a=3.116.S=8.2 by using FindRoot and I got that w= 2548.33 but when I used this value I did not get zero for the determinte and that which made me puzzled and confused added to that the right value of w should be 3426 as what is written in the research