# Solve the IVP (3x-y) \frac{dy}{dx} = y+2x, y(1)=1. You should give an explicit solution whenever...

## Question:

Solve the IVP

{eq}(3x-y) \frac{dy}{dx} = y+2x {/eq}, y(1)=1.

You should give an explicit solution whenever it is possible.

## Homogenous Differential Equations:

A homogenous differential equation is an equation in the form of {eq}\frac{dy}{dx}=f\left(\frac{y}{x}\right) .{/eq} The advantages of having homogeneous differential equation is that it can always be reduced to a separable equation by means of a algebraic substitution and manipulation.