we are given the laplacian:(adsbygoogle = window.adsbygoogle || []).push({});

(d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's

u=0 for (-1<y<1) on x=0

u=0 on the lines y=plus or minus 1 for x>0

u tends to zero as x tends to infinity.

Using separation of variable I get the general solution

u = (ax+b)(cy+d) + sum over k of (Ak*sinky + Bk*cosky)*(Ck*exp(kx) + Dk*exp(-kx))

where a,b,c,d,Ak,Bk,Ck,Dk are constants. We can then say that Ck = 0 from B.C's, and I also think that we can say that a=b=c=d=0 as well (but I am not sure). I'm having trouble imposing the rest of the B.C's. the final solution is

u=sum over m of [Am*cos(m*Pi*y/2)*exp(-(m*Pi*x/2)

thanks very much

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: P.d.e problem

**Physics Forums | Science Articles, Homework Help, Discussion**