It is my first week dealing with Differential Equations, and I am lost at the following question:

Show that the equation $P(x,y)dx+Q(x,y)dy=0$ has an integrating factor of type $μ\frac{y}{x}$ if and only if the expression $x^2\frac{P_y-Q_x}{xP+yQ}$ depends on $\frac{y}{x}$ only.

Relying on the above, resolve the following initial value problem, including its domain of definition: $(4x^5y^2+x^4e^x+2x^3e^x-\frac{3x}{y^2})dx+(4x^6y+\frac{2x^4e^x}{y})dy=0$

$y(1)=-\sqrt\frac{e}{2}$

- Serverfault Help
- Superuser Help
- Ubuntu Help
- Webapps Help
- Webmasters Help
- Programmers Help
- Dba Help
- Drupal Help
- Wordpress Help
- Magento Help
- Joomla Help
- Android Help
- Apple Help
- Game Help
- Gaming Help
- Blender Help
- Ux Help
- Cooking Help
- Photo Help
- Stats Help
- Math Help
- Diy Help
- Gis Help
- Tex Help
- Meta Help
- Electronics Help
- Stackoverflow Help
- Bitcoin Help
- Ethereum Help