First, do you know what the "assumptions of the Cauchy-Kovaleski theorem" are?
"A Taylor series of order less than or equal to 2 about the origin", in two variables, x and t, is \(\displaystyle u(x, t)=Ax^2+ Bt^2+ Cxt+ Dx+ Et+ F\) for some contants, A, B, C, D, E, and F. What are \(\displaystyle u_x\) and \(\displaystyle u_t\). Put those into the equation.
