(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

solve u_{xx}= u_{tt}

3. The attempt at a solution

using the method of separation of variables I get

X''(x) - λ*X(x) = 0

T''(t) - λ*Τ(t) = 0

For λ = 0 I get X(x) = Ax + B where A and B are constants

T(t) = Dt + E where D and E are constants

hence u(x,t) = (Ax + B)*(Dt + E)

for λ>0 I get u(x,t) = [PLAIN]http://img690.imageshack.us/img690/8068/asdqu.gif [Broken] [Broken][/URL] where c1,c2,C1,C2 constants

for λ = -b^2<0 I get (E*cos(bx) + F*sin(bx))*(G*cos(bt) + H*sin(bt)) where E,F,G,H constants

hence the solution

is from the superposition principle

u(x,t) = (Ax + B)*(Dt + E) + [PLAIN]http://img690.imageshack.us/img690/8068/asdqu.gif [Broken] [Broken][/URL] + (E*cos(bx) + F*sin(bx))*(G*cos(bt) + H*sin(bt))

please is this correct? i think its wrong, because im not sure about the last part

also our professor has only the [PLAIN]http://img690.imageshack.us/img690/8068/asdqu.gif [Broken] [Broken][/URL] as a reply, but i think its wrong, because we have to check for all λ to find all the possible solutions

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

Join Physics Forums Today!

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

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

# Homework Help: Partial differential equation

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