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I'm hitting a brick wall with $\dfrac{dx}{ds} = 1-y^2$. Is it possible for me to let $c = 1-y^2$?

Would appreciate any help.

ASB
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guest
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  • Are you using method of characteristics? – science Mar 14 '15 at 05:48
  • Yes, my class is currently being "taught" to use the MOC – guest Mar 14 '15 at 05:52
  • I just posted an answer for you. – science Mar 14 '15 at 05:53
  • You seem to have multiple problems with the exercise and you asked multiple questions about characteristics already. Please edit your question to elaborate what you've tried so far and at which point exactly you don't know how to proceed further. – Three.OneFour Mar 14 '15 at 09:41
  • I will do so. The reason why my attempt was not posted was because I have not learned LaTeX and the LaTeX language generated by Mathematica was not working on MathStack. The real reason why I'm grappling with this chapter(and very possible this current unit) is because of a terrible lecturer I'm having this semester as an exchange student. In my home University, we would be presented with the theorem, followed by proof, and, an example. In this class, there is no theorem nor proof and notations made explicit. I've already spent more than 50 hours in 2 weeks trying to get my head around. – guest Mar 15 '15 at 01:19
  • A case in point is the proper denoting of notation. I frequently see the use of x(0) = some constant of integration. As a student new to more advance topic on PDE, x(0) is confusing but such confusion can be reduced by writing (x(x_0),t(s)) = (x(x_0),0). The proper way for any respectable lecturer to teach is to present first the theorem, proof and an example. I assure you I'm not the only lost soul as my observation tells me that if every students are "copying" down solutions during the tutorial (by the lecturer), something is awry wrong! – guest Mar 15 '15 at 01:25
  • I shall add that I consider myself to be an average student but who is hardworking and learn exceedingly fast given the right parameters. While I had made attempts, there are times I feel really lost that I could hardly begin to make explicit the issue I face. The burden of proof lies on me to commute my attempt but this is indeed difficult without having the time to learn LaTeX. Let's just say I have learn more on this site (even if the solution is given) than trying to make sense of what the lecturer is lecturing. – guest Mar 15 '15 at 01:33

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You can use separation of variables to solve $\frac{dx}{ds} = 1-y^2 $ as

$$ x= (1-y^2 )s+k. $$

science
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  • The other brick wall is also du/ds.

    On my solution it says: u(x,y,0)= e^(y-x0)^(2) then, u(x,y,t) = e^(y-(x+(y-1)^(2)t)^(2)) which I clearly have some problem wrapping my head around. If you would help me.

     – guest Mar 14 '15 at 06:14
  • Check this problem. – science Mar 14 '15 at 06:18