So the maximal solution was basically just asking on what open interval is the explicit solution maximized (so basically the maximum domain on which it is defined on) on including the original initial condition. What really confused me though is the fact that there is an infinite amount of...
Find the value of a ∈ R for which the initial value problem:
(S) {(xy' +y)/(1+x2y2)=1
{y(0)= a
has a solution and, for this value of a, find explicitly the maximal solution of (S).
I'm assuming I first find the implicit solution of the original diff eq (which I'm not too sure how to do...
Looking at my notes, 0 is supposed to be included because its a solution to begin the problem, yet 0 is undefined in this specific case if the above explicit solution is correct. So, I'm a bit confused even more so now.
Okay so I implicitly solved it and got:
exy-sin(x)=1
Then I was able to pretty easily solve it explicitly from there:
$$y=(ln|1+sin(x)|)/x$$
Now after this I need to find the maximal open interval and that's where I'm really really stuck.
I need to find the explicit maximal solution of an IVP using exact Diff Eqs:
The IVP is given as:
{xexyy'-cos(x)+yexy=0
{y(0)=1
So I know at first I need to get the implicit solution by getting that:
A(x,y) = xexy
B(x,y) = -cos(x)+yexy
I know I need to find the partial derivative of A(x,y)...
Thank you Chris! Once explained I realized how easy they actually were, just was frustrated never seeing anything of the sort before that wasn't quite sure how to get started.
I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just don't want it to seem like I'm...
I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just don't want it to seem like I'm...
Thank you so much for the help and linking me to this website! I'm sure I will be using it a lot this semester because I can hardly understand my professor in diff eq. This helped a lot though and made me realize where I made my original mistake. Again thanks so much!