Question

What is a solution to the differential equation `dy/dx=x/y`?

Answer 1

`y^2 = x^2 + C`

Explanation:

`dy/dx = x/y`

This is a First Order Separable Differential Equation, we can "separate the variables" to give;

`intydy = intxdx`

Integrating we get:

`1/2y^2 = 1/2x^2 + A`
`:. y^2 = x^2 + 2A`
`:. y^2 = x^2 + C`