Solve the differential and initial value problem:

Question

x(dy/dx) + 1 = y^2

y(1)=0

I tried using bernoulli and it didn't quite work.

Answer 1

xy' + 1 = y^2
xy' = y^2-1
y' = (y^2-1)/x
dy/(y^2-1) = dx/x
arctanh(y) = log(x)
or,
log (1-y)/(1+y) = 2log(x)+c

and you can massage that into exponentials and wind up with

y = 1-e^(2cx^2) / 1+e^(2cx^2)