1. The problem statement, all variables and given/known data Solve u_t -k u_xx +V u_x=0 With the initial condition, u(x,0)=f(x) Use the transformation y=x-Vt 2. Relevant equations The solution to the equation u_t - k u_xx=0 with the initial condition is u(x,t)=1/Sqrt[4[itex]\pi[/itex] kt] [itex]\int[/itex] e^(-(x-y)^2 /4kt)f(y) dy 3. The attempt at a solution I really just need help subbing in the change in variable. I think it's something like u_y= u_t dt/dy +u_x dx/dy with dx/dy=1/(dy/dx)=1, dt/dy=1/V =-1/V u_t +u_x But this doesn't put the equation into a useful form... the other thing I thought of was u_x=u_t dt/dx +u_y dy/dx =0+u_y and u_t=u_x dx/dt+u_y dy/dt =-Vu_y And then we have that u_t+V u_x=-V u_y +V u_y=0, so the DE is just k u_xx=0; which I'm guessing isn't right either - because then it's just straight integration; (with the constants as functions of y?)... Anyway, I'm fairly sure that the change of variables will result in either u_y=u_t+V u_x or possibly some multiple.