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.

How to solve the PDEs with more than two independent variables whose their most-general solutions are known?

For example the PDE $u_{xxx}+u_{yyy}+u_{zzz}-3u_{xyz}=0$ , according to does this PDE have a name?, the most-general solution is $u(x,y,z)=F_1(y-x,z-x)+F_2\left(y-\left(-\dfrac{1}{2}+\dfrac{i\sqrt{3}}{2}\right)x,z-\left(-\dfrac{1}{2}-\dfrac{i\sqrt{3}}{2}\right)x\right)+F_3\left(y-\left(-\dfrac{1}{2}-\dfrac{i\sqrt{3}}{2}\right)x,z-\left(-\dfrac{1}{2}+\dfrac{i\sqrt{3}}{2}\right)x\right)~.$

If I have the conditions $u(0,y,z)=f(y,z)$ , $u_x(0,y,z)=g(y,z)$ and $u_{xx}(0,y,z)=h(y,z)$ , how can I find $F_1$ , $F_2$ and $F_3$ ?

share|improve this question
add comment

Your Answer


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

Browse other questions tagged or ask your own question.