1. ## Differential Equation Problem

(x+y) * (dy/dx) = (x-y)

the given answer is y^2-2xy-x^2 = C

The problem is in a section of the textbook where substitution methods are taught. That is, making a subsitution where v = some term containing the variables x and y. Then solving the substitution equation so that y = some term containing the variables x and v. Taking the derivative of that term so dy/dx can be substituted for. Then the next step would be to separate the variables x and v. integrate, and lastly you substutite x and y back in for v to gain your solution to the Diff EQN.

Problem is, I can't do it.

Help is much appreciated!

JB

2. Originally Posted by jblorien
(x+y) * (dy/dx) = (x-y)

the given answer is y^2-2xy-x^2 = C
First rewrite your equation as follows:

$\displaystyle \frac{{dy}} {{dx}} = \frac{{x - y}} {{x + y}}.$

Now multiply top & bottom by $\displaystyle \frac1x,$

$\displaystyle \frac{{dy}} {{dx}} = \frac{{1 - \dfrac{y} {x}}} {{1 + \dfrac{y} {x}}}.$

Now it remains to substitute $\displaystyle y=ux.$

3. Thank you