text a find characteristics for the pde describing u t x text for t in

Question

\text { a) Find characteristics for the PDE describing } u(t, x) \text { for } t \in \mathbb{R} \text { and } x \in \mathbb{R} \frac{\partial^{2} u}{\partial t^{2}}+\frac{\partial^{2} u}{\partial t \partial x}-2 \frac{\partial^{2} u}{\partial x^{2}}=t hence find that the general solution (b) Find the solution that satisfies the initial conditions u(0, x)=0, \quad u_{t}(0, x)=0