- #1

drcameron

- 4

- 0

## Homework Statement

Find the general solution of the following homogeneous differential equations:

(i) [tex]\frac{du}{dx} = \frac{4u-2x}{u+x}[/tex]

(ii) [tex]\frac{du}{dx} = \frac{xu+u^{2}}{x^{2}}[/tex]

(You may express your solution as a function of u and x together)

## Homework Equations

There are no relevant equations to this solution

## The Attempt at a Solution

(i) [tex]\frac{du}{dx} = 4 - \frac{6x}{u+x}[/tex]

I could then use the substition y=u+x with dy/dx = du/dx + 1 to give:

[tex]\frac{dy}{dx} = 5 - \frac{6x}{y}[/tex].

Now I'm really lost as shouldn't the y be on the top or am I missing something really stupid here?

(ii) Similar problem to above - should get it from (i) but a hint would go a long way.