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-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)
this is tough to type in without an equation editor, (du/dx) denotes the partial derivative of u with respect to x, (du^2/dt^2) denotes the second partial derivative of u with respect to t, etc.
anyways, this is a model equation from my finite element analysis class
When b=0, c2=0, co=0, c1=rho*A, a=kA
this equation represents unsteady heat transfer in a fin
When a=0, b=E*I, co=k, c1=0, c2=rho*A
this equation represents transverse vibrations in a beam
When a=E*A, b=0, c1=0, c2=rho*A, co=0
it represents longitudinal motion(vibration or wave propogation) of a slender rod
all of these require initial conditions and boundary conditions to be specified, but that would have been alot more typing and i think it looks intimidating enough already
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When motors stall, bad things happen. - Rob Stehlik [more] 
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