I'm watching a KhanAcademy video. The question is to solve the exact diff. eq.

All of the steps are (obviously) fine and he comes up with

which he then uses to say the solution is

I understand those steps, too (well, I think I do).But what is that solution? Is that y?The solution to a diff. eq. should be a function, y, whic, when you take its derivatives, satisfies the original equation.

So what was ? Is it just a which solved the original? Can I say that [tex]\psi(x,y)=y_g(x,y)[\tex]? Note that if I add the partial of wrt x to the partial wrt y times y', I get the original question back.

I'm not really sure how to ask my question. Does it make sense? Think of this question like a beginning algebra student asking what it means that is the solution to . You answer that question by telling him to plug 5 back into the original equation.)