Thread: Solve du/dt + 2du/dx=-u for u(x, t)

hi guys, having trouble completing this equation

du/dt + 2du/dx=-u
solve for u(x,t)

for initial conditions t=0 and u=1 for x<0 and u=0 for x>0
once solving the equation do i give 2 solutions? one for u=1 and the other for u=0?
if any one has an idea of how to get started with the diff equation it would be much appreciated.

thanks in advance

Originally Posted by b0mb3rz

hi guys, having trouble completing this equation

du/dt + 2du/dx=-u
solve for u(x,t)

for initial conditions t=0 and u=1 for x<0 and u=0 for x>0
once solving the equation do i give 2 solutions? one for u=1 and the other for u=0?
if any one has an idea of how to get started with the diff equation it would be much appreciated.

thanks in advance

This qualifies as a first order quasilinear PDE, so you can use the method of characteristics.

-Dan