Solving PDE Problem: du/dt+du/dx=0 with Initial Condition u(x,0)=xe-x2

[pentazoid]

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?

 

[the1ceman]

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?

One way of solving a pde like that is to always try separation of variables , so that you assume$$u(x,t)=X(x)T(t)$$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!