I'm getting a incorrect answer for Given 2xy(dy/dx) + y^2 - 1 = 0 find solution A) (1,0) B) (0,1) in x-y plane. Please tell me where i'm screw up and how to fix it.
This is my workout:
2xy(dy/dx) + y^2 - 1
y^2 +2y dy=-2x + 1 dx
(y^3/3)+(y^2) = x-(x^2) +C
This is where my problem is, I'm not sure from here how to do the following.
-divide through by y
y=square root (-x+C/y+3) I don't think that is right and if it is what is my next step in getting rid of y on the right side?
Still not getting the correct answer. Please tell me where i went wrong and how to fix it. So i took the intergal as given by Prove It:
-ln(y^2-1) = ln(x) + C
-solve for y have to remove the ln by using e
e^(-ln(y^2-1)) = e^(ln(x) + C) => (1/(y^2)-1) = xe^C
y=squart root x(e^C/2)