How do you solve this differential equation: y' = [x / (y+2)]?

As stated, the equation is: y' = [x / (y+2)]



The instructions for the problem from the text:

"... find the general solution of the indicated differential equation. If possible, find an explicit solution."



The text is: Differential Equations, 2nd Edition

Authored: Polking, Boggess, and Arnold

Published: Pearson Prentice Hall



My process so far:

y' = [x / (y+2)]

dy / dx = [x / (y+2)]

(y+2)*dy = x*dx

鈭?y+2)*dy = 鈭玿*dx

(y^2 / 2) + 2y = (x^2 / 2)

1/2(y^2 + 4y) = (x^2 / 2)

y^2 + 4y = x^2



And this is where I am stuck. It's been 2 years since I last took a computational math class and I have forgotten how to solve this. The solution provided by the text is this:

y(x) = -2 卤 鈭?x^2 + E)How do you solve this differential equation: y' = [x / (y+2)]?
you forgot the C constant when you intergrated both side. Please let me complete it



y' = [x / (y+2)]

dy / dx = [x / (y+2)]

(y+2)*dy = x*dx

鈭?y+2)*dy = 鈭玿*dx

(y^2 / 2) + 2y = (x^2 / 2) +C1

1/2(y^2 + 4y) = (x^2 / 2) + C1

y^2 + 4y = x^2 +C1



y^2 + 4y + 4 = x^2 +C //C = C1+5

(y+2)^2 = x^2 + C



y+2 = 卤鈭?x^2 + C)

or

y = -2 卤 鈭?x^2 + C)