2. Consider the following equation for u(x, y) x \frac{\partial^{2} u}{\partial x^{2}}+3 x^{3} \frac{\partial^{2} u}{\partial x \partial y}-18 x^{5} \frac{\partial^{2} u}{\partial y^{2}}+\left(x^{3}-2\right) \frac{\partial u}{\partial x}+6 x^{5} \frac{\partial u}{\partial y}=0 (a) Assuming x 0 classify this equation and show that its characteristic equations aregiven by \xi=y+x^{3}, \quad \phi=y-2 x^{3} Use these characteristics to show that the equation reduces to the standard form: 9 \frac{\partial^{2} u}{\partial \xi \partial \phi}-\frac{\partial u}{\partial \xi}=0 (c) Hence find the general solution for u(x, y).