Solve

1. Consider the solution u(t,x) of the initial value problem w= u?+u2, u(0,x2) = cosa. oo a) Find the expansion u(t,2) = 57 ul*l(x)t* about t=0 upto O(t"). k=0 t + cos = b) Find the expansion ae = S f\\*l\\(c)t* about t=0 up to O(t7). k=0 Compare it with the expansion of u(t,2) determined in item a). t{+cos 2x c) Verify that u(t,2) = _ is the exact solution of the initial value