Question

How to you find the general solution of `dy/dx=x/y`?

Answer 1

`x^2-y^2=c`

Explanation:

`dy/{dx}=x/y`

`ydy=xdx` by exploiting the notation (separation)

`int ydy=int xdx` further exploiting the notation

`1/2y^2=1/2x^2+d`
`y^2=x^2+2d`
`x^2-y^2=-2d`
`x^2-y^2=c` where `c=-2d`
Depending on whether `c` is positive, negative or zero you get a hyperbola open to the `x`-axis, open to the `y`=axis, or a pair of straight lines through the origin.