How to solve the following system of partial differential equations? I have a system of partial differential equations:
\begin{align}
& u(a,b,c) \frac{\partial y}{\partial c} = \frac{4}{3} ab, \\
& u(a,b,c) \frac{\partial y}{\partial b} = \frac{2}{3} ac + 2 b^2, \\
& u(a,b,c) \frac{\partial y}{\partial a} = \frac{4}{3} bc.
\end{align}
I tried to solve it using maple as follows. First I define
\begin{align}
pde := u(a, b, c)*(diff(y(a, b, c), c)) = (4/3)*a*b, \\
u(a, b, c)*(diff(y(a, b, c), b)) = (2/3)*a*c+2*b^2, \\
u(a, b, c)*(diff(y(a, b, c), a)) = (4/3)*b*c
\end{align}
Then I use the command: pdsolve(pde). But there is an error. How to solve this system of equations using maple? Any help would be greatly appreciated!

The command "pdsolve([pde]);" can solve this system of partial differential equations.
