Problem B:
a) Verify that the function u(t,x) = sin(sin(t+x)) is a solution of the transport equation
u_{t}(t,x) = u_{x}(t,x). b) Verify that the function f(x,y) = 3 y^{2}+x^{3} satisfies the Euler-Tricomi partial differential equation u_{xx} = x u_{yy}. 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. |