# PDE Question

1. Jan 21, 2006

### dglee

For some reason i can't post in the calculus and beyond section :grumpy:
but i was hoping someone could help me with this question
eq.1 du/dt - fv = g*(dn/dx)
eq.2 dv/dt + fu = g*(dn/dg)
eq.3 du/dx+dv/dg=(1/(H)*(dn/dt)
manipulate the equations to derivate a single PDE in one variable n which is fourth order in time.
the hint was given eliminate u from (1) and (2) and from (1) and (3). Then eliminate v.
ok i was told to do this question by some sort of linear row reducing type of method
eq.1 (d/dt)*u - (f)*v = (g*d/dx)*n
eq.2 (f)*u + (d/dt)*v = (g*d/dg)*n
thus
eq.1 f*((d/dt)*u - (f)*v = (g*d/dx)*n)
eq.2 d/dt*((f)*u + (d/dt)*v = (g*d/dg)*n)
eq.1 (f*d/dt)*u - (f^2)*v = (f*g*d/dx)*n
eq.2 (f*d/dt)*u + (d^2/dt^2)*v = (g*d^2/dg*dt)*n
so i can eliminate u
then becomes
(-f^2-d/dt)*v = (f*g*d/dx - g*d^2/dg*dt)*n
so i did the same thing for 1 and 3. then i tried to eliminate v, but however i can't. Im not even sure if i even eliminiated u properly.

Last edited: Jan 21, 2006