The discussion focuses on solving the partial differential equation (PDE) du/dt + du/dx = 0 with the initial condition u(x,0) = xe^(-x²). The solution provided is u(x,t) = (x-t)e^(-(x-t)²). A recommended method for solving such PDEs is the separation of variables technique, where the solution is expressed as a product of functions of x and t, specifically u(x,t) = X(x)T(t).
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One way of solving a pde like that is to always try separation of variables , so that you assumeu(x,t)=X(x)T(t)where X is just a function of x and T just a function of t, plug this into your pde and see what u get!pentazoid said:Homework Statement
which solutions of du/dt+du/dx=0 is equal to xe-x2
Homework Equations
The Attempt at a Solution
u(x,0) = xe-x2
u(x,t)= (x-t)e(-x-t)2
what else do i need to do?