Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 1

(dy)/dx = x/y
This differential equation is separable since it can be re-written in the form

N(y)dy = M(x)dx
So separating the variables, the equation becomes
ydy = xdx
Integrating both sides, it result to
int y dy = int x dx
y^2/2 + C_1 = x^2/2 + C_2
Isolating the y, it becomes
y^2/2 =x^2/2+C_2-C_1
y^2=x^2 + 2C_2 - 2C_1
y=+-sqrt(x^2+2C_2-2C_1)
Since C2 and C1 represents any number, it can be expressed as a single constant C.
y = +-sqrt(x^2+C)

Therefore, the general solution of the given differential equation is y = +-sqrt(x^2+C) .