Question

How do you find the general solution of the differential equation: `dy/dx=(3x)/y`?

Answer 1

`y = +-sqrt(3x^2 + C`, (where `C` is arbitrary constant).

Explanation:

We have:

`dy/dx = 3x/y`

This is a First Order separable Differential Equation, so we can just collect terms in `y`, and terms in `x` and "separate the variables" to get:

`int \ y \ dy = int \ 3x \ dx`

We can now integrate to we get:

`\ \1/2y^2 = 3/2x^2 + C'`
`:. y^2 = 3x^2 + C`, (where `C` is arbitrary constant).
`:. y \ \ = +-sqrt(3x^2 + C)`, (where `C` is arbitrary constant).