APM346-2022S > Chapter 2

f(x) in Method of Characteristics

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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)

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