Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For an equation of the form $\displaystyle f\left(\frac{\partial z}{\partial x}, \frac{\partial z}{\partial y}\right) = 0$ the complete solution is $ z = ax + \phi (a) y + \psi(a)$--(1) and general solution is given by eliminating a between (1) and $\displaystyle \frac{\partial z}{\partial a} = 0$. I don't get it how. Can anyone help me by giving me an example with particular problem below?

Let, $3p^2 - 2 q^2 = 4pq$ where $p$ and $q$ are $x$ and $y$ partial derivatives of $z$ respectively. The complete solution is given by $\displaystyle z = a \left( x + \frac{3}{ 2 \pm \sqrt{10}} y\right) + k$. How to find general solution for this particular problem?

share|improve this question
    
The first sentence doesn't make sense: are there additional conditions on the function $f$ that you didn't tell us? –  Willie Wong Sep 3 '12 at 13:23
    
Also, if this is coming from a textbook, can you state which textbook you are using, and if possible include how the textbook/lecture notes/paper defines "complete solution" and "general solution"? –  Willie Wong Sep 3 '12 at 13:25

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.