f(x) in Method of Characteristics

[Yifei Hu]

In solving the problem $2U_t+3U_x=0, U(0,x)=f(x)$, tutorial gave answer $U=f(x-\frac{3}{2}t)$ while I have $U=f(3t-2x)$. Are both answers valid? We can use different form of C as long as it represent the same family of characteristics right?

[Victor Ivrii]

Yes, there are many answers which are correct because they include arbitrary functions (and in ODE arbitrary constants)