What is the solution of the Cauchy Problem pde u_t-uu_x=0

Question : What is the solution of the Cauchy Problem pde \[u_t-uu_x=0\ ,\ \ x\in R,\ t>0\] \[u\left(x,0\right)=x,\ \ x\in R\]Solution :For the given Cauchy Problem pde\[u_t-uu_x=0\ ,\ \ x\in R,\ t>0\] \[u\left(x,0\right)=x,\ \ x\in R\]Substituting x=x, t=y, u=zThe characterstics…

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