I have worked this problem but somewhere I missed something and I\'m not sure wh

Question

I have worked this problem but somewhere I missed something and I'm not sure where I did:

y'= 2x/y+x2y y(0)=-2 which becomes: dy/dx= 2x/y(x2 + 1) integrating both sides: y2 / 2= ln(x2+1)+c so now solve for C: y2 / 2 - ln(x2+1)= C substitute y(0)=-2: (1/2)- ln(0 + 1) = c, therefore (1/2)= c. So now the equation is   y2 / 2 = ln(x2+1)+(1/2) and: y= ln(x2 +1)(1/2) its close to the answer in the book but not right? why=[
y'= 2x/y+x2y y(0)=-2 which becomes: dy/dx= 2x/y(x2 + 1) integrating both sides: y2 / 2= ln(x2+1)+c so now solve for C: y2 / 2 - ln(x2+1)= C substitute y(0)=-2: (1/2)- ln(0 + 1) = c, therefore (1/2)= c. So now the equation is   y2 / 2 = ln(x2+1)+(1/2) and: y= ln(x2 +1)(1/2) its close to the answer in the book but not right? why=[

Explanation / Answer

y(0)= -2 -[2 ln(x^2 + 1) + y^2/2=0 (eq.1) -{2 Ln(0^2+1)+(-2)^2] ....plug those in and get c. then go back to eq.1 and put c there to get in terms of y.

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