Hello. I have to find,with Maple, the solution of the diff equation E=(1+x^2)*(dy/dx)^2+y(x)^2,

when E=1 and the initial condition y(0)=0.

I also have to plot my solution(s) over the range 0<=x<=12 and also plot y against log(x) for 1<=x<=10^4.

My solution is:

E:=(1+x^2)*(diff(y(x),x))^2+(y(x))^2;

Then dsolve({E=1,y(0)=0},y(x));

I gained two solutions that were Rootof(something with ln, arctan, Z, Pi etc)

After I used the plot command to plot the two solutions, but took Maple 7 minutes to plot them and plotted something very strange.

Then I tried to plot the two solutions of the diff.equation and ln(x) in the same axis but after 2 minutes Maple wrote an error as following:

"Warning, unable to evaluate 2 of the 3 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

I don't know what went wrong and if I did anything wrong when I was writing the diff equation. I found it very strange that Maple took 7 minutes to plot the first graph (and my pc has very good specifications).

If someone can tell me if i did something wrong I will appreciate it! Thank you very much!