Find the solution(s) of the differential equation E=(1+x^2)*(dy/dx)^2+y(x)^2, when E=1 and the initial condition y(0)=0 is imposed.

Plot your solutions oner the range 0<=x<=12, also plot y against log(x) for 1<=x<=10^4. Comment on the number of solutions obtained and their relation to each other.

Find the first three zeros of y(x) to 2.s.f (that is, xc such that y(xc)=0)

My solution:

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