Question

Find an integrating factor for y*dx-x*dy=0 and solve the equation.

Answer 1

@SithsAndGiggles

Answer 2

Whoops, sorry, forgot about that negative...
\[y-x\frac{dy}{dx}=0\]
Partial derivatives:
\[\frac{\partial}{\partial y}y=1\\
\frac{\partial }{\partial x}x=-1\]
Integrating factor:
\[\log\mu(x)=\int\frac{1-(-1)}{-x}~dx=-2\int\frac{dx}{x}~~\implies~~\mu(x)=e^{-2\ln x}=\cdots\]

Answer 3

When you take the partial derivative, isn't it d/dx(-x)=-1 instead of d/dx(x)=-1?

Answer 4

Yes, sorry. Minor editing error :P

Answer 5

Thank you so much! I apologize for the slowness of my computer. Please be excused.

Answer 6

Don't worry about it, and you're very welcome!