text: # Find solution to exact ODE: $(4bxy(x)+3x+5)\dot{y}+3x^2+8ax+2by(x)^2+3y(x)=0\hspace{0,5cm}a,b\in\mathbb{R}$
  
  So I have this exact ODE
  
  $$(4bxy(x)+3x+5)\dot{y}+3x^2+8ax+2by(x)^2+3y(x)=0\hspace{0,5cm}a,b\in\mathbb{R}$$
  
  I already managed to show that $$F=2bxy^2+3xy+5y+x^3+4ax^2$$.
  
  Now, how can I find the solution $$y$$ ? Seperating the variables is not really an option and it's also not linear. I'm kind of hitting a wall.
  
  The solution to the ODE is $$F=c\implies2bxy^2+(3x+5)y+(x^3+4ax^2)=c$$, where $$c$$ is a constant. This is a quadratic equation in $$y$$ so you can use the quadratic formula to express $$y$$ as an explicit function of $$x$$, if it is really required.