a) Verify that the function u(t,x) = sin(sin(t+x)) is a solution of the transport equation
ut(t,x) = ux(t,x).|
b) Verify that the function f(x,y) = 3 y2+x3 satisfies the Euler-Tricomi partial differential equation uxx = x uyy. This partial differential equation is useful in describing transonic flow. Find an other solution which is not a multiple of the solution given in this problem.