tymo

thanks i got it! i can use b so it will fit the rest of theorem, not the other way around. thanks again!

Well I did read it again, and I think I am missing it, I looked at an example where they gave -\infty <y <\intfy, there they used the fact that |f(x,y)| <= K, if I apply that to my problem : Can I make the rectangle then dependent of y? Then I could take b = y^2 and thus M = y^2 +1. but then still: minimum of 1/2 and (y^2 / y^2 +1), and that is not a definite minimum? I mean its 1/2 for y>1, but for y<1 y^2/y^2+1 is the minimum... I think I'm missing a step or I'm thinking too difficult ?

Hey guys, I am a bit new to this forum and this is my first post (i used to just read stuff that came up here). I hope its not inappropriate to ask something right away, because i will do now ask for any advice. I'm studying applied mathematics, and at the moment im working on differential equations. Now i found something i could find an answer to in my book, or somewhere else on the internet. In my textbook (martin braun, differential equations and their applications), i stumbled on to the following question: Show that the solution of y(t) of the given initial-value problem exists on the specified interval: y' =y^2 + cos(t^2) , y(0)=0; on the interval 0 <= t<=1/2. the existence-theorem on this subject tells me that I need a rectangle [t_0 < t < t_ +a ] X [y_0 -b , y_0 +b] to be able to use the theorem. But, thats my problem here, I can't construct a proper rectangle, because there's no |y(t)| <=b specified. Now my question is, how do I apply the existance theorem to a initial value problem when the specified interval has boundairies for t, but not for y. (if i use my own brain, i'd say just use |y| <= \infty, but i cant justify that) Could anyone point me in the right direction or give me a helpful answer? Would be great! x tymo

hi! im new here and i think it would be appropriate to introduce I'm Tymo and I study applied mathematics, and I like science in general, and well, without trying to be a streber, i like to learn about a wide range of things. (that doesnt mean i am a great student, because I am not, not putting enough time in my study I guess) anyway, i am curious about what i will find here and be able to discuss with you. I will probably ask for help on things I see in my books or homework also. see ya!