Originally posted by joe shmoYou can rewrite the differential equation as:
yeah, apparently Laplace transforms are ?only? good for DE's with constant coeficients?
I guess the way to go about this one is using integration factor method for first order linear ODE's.
Can anybody show me why the Laplace doesn't supposedly work for non-constant coeficients?
p dh/dp + h - RT/g = 0
dh/dp + h/p - RT/(gp) = 0
Again, you should probably nondimensionalize the equation here, but I'm too lazy to that for you.
The Laplace transform of h/p is an integral over H(s). You don't get an algebraic equation in H(s).
1 edit
Originally posted by KazetNagorraI see that I incorrectly assumed that
You can rewrite the differential equation as:
p dh/dp + h - RT/g = 0
dh/dp + h/p - RT/(gp) = 0
Again, you should probably nondimensionalize the equation here, but I'm too lazy to that for you.
The Laplace transform of h/p is an integral over H(s). You don't get an algebraic equation in H(s).
L{t*f'(t)} = L{t}*L{f'(t)}
I realized this after I "tried" to use the definition to derive the transform.
After fruitlessly atempting those integrals,I found a therom that adresses the non-constant coeficients, and to no avail the transform is itself still a 1st order, linear differential equation, that has to be solved by intergation factor methods, with limits, and the whole nine yards.
noticing the form of the equation in the first place would have saved me a headache, but indirectly, im glad I took the scenic route.
Thanks for your help!
Eric