# Thread: Differential Equation<don't know what method to use

1. ## Differential Equation<don't know what method to use

Code:
(x^2+y^2-5)dx=(x+xy)dy
What method should I use to find the General Solution of this?

2. ## Re: Differential Equation<don't know what method to use

Originally Posted by shinmei
Code:
(x^2+y^2-5)dx=(x+xy)dy
What method should I use to find the General Solution of this?
Well my (admittedly limited) differential equation library comes up with nothing. Neither does Wolfram|Alpha. That's hardly the last word but I'd say you're going to need an approximation technique.

-Dan

3. ## Re: Differential Equation<don't know what method to use

$\displaystyle (x^2+y^2-5)dx=(x+xy)dy$

$\displaystyle \frac{dy}{dx}(x+xy)=x^2+y^2-5$

$\displaystyle \frac{dy}{dx}=\frac{x^2+y^2-5}{x+xy}$

$\displaystyle \int \frac{dy}{dx} dx=\int \frac{x^2+y^2-5}{x+xy} dx$

$\displaystyle \int dy=\int \frac{x^2+y^2-5}{x+xy} dx$

dy is the same as 1.dy, and so integrating 1 (which is congruent to $\displaystyle y^0$) with respect to y will give you $\displaystyle \frac{y^1}{1} = y$

$\displaystyle y=\int \frac{x^2+y^2-5}{x+xy} dx$

Unfortunately, my high school understanding of calculus doesn't give me a method to integrate the RHS of this equation. If someone here could do that then you should have your general solution. I have no idea if this is correct though, just a long shot.

4. ## Re: Differential Equation<don't know what method to use

^ the problem to me seems to be separating the unknowns $\displaystyle x$ and $\displaystyle y$ onto the different sides of the equation. I can't seem to factorise them myself.