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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Over 15 years teaching at the college level.
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
| User | Date | K | C | T | P | Comments |
|---|---|---|---|---|---|---|
| Grisel | 07/26/09 | 10 | 10 | 10 | 10 | Thanks!! that was very helpful |
| Warm | 07/11/09 | 10 | 10 | 10 | 10 | Thanks |
| Dan | 01/14/09 | 10 | 10 | 10 | 10 | |
| Ambika | 07/23/08 | 10 | 10 | 10 | 10 | Thanks for your answer. |
| Cheryl | 07/10/08 | 10 | 10 | 10 | 10 | I feel dumb. For some reason ..... |
Hello Debraj, Sorry for my delay. I tried to get my CAS (computer algebra system), Maple 12, to solve your system of DE's...but it failed. Perhaps if you could furnish some actual values for the
dV/dt=20-k*h^2, based on the info given in the problem. However, V=(4/3)h^3, thus, dV/dt=4*h^2*dh/dt. Now substitute that into the first equation to get: 4*h^2*dh/dt=20-k*h^2. Dividing by 4*h^2 yields:
1. Re-written as: y'' + (x^2-1)/(x^2(x+1)) y' - y/(x^2(x+1)) = 0 . Singular points where x^2(x+1)=0...thus x=0 and x=-1 are singular pts. . Since lim (as x->0) x[(x^2-1)/(x^2(x+1))] DNE, x=0 is an
Let y=e^(rx), so we get the characteristic equation: r^2-4r+4=0 ==> (r-2)(r-2)=0 ==> r=2,2 Repeated root, so the general solution is: y(x)=(A+Bx)e^(2x) Now impose the IC's: y(0)=0 ==> 0=(A+0)e^0
Hello, Wow, that's a tough one! Let me just make sure, the problem is: Integrate[dx/(e^(-k1*x)+k2*x+k3)] - yes? If so, then I'm afraid I cannot help, even Maple 12 and Mathematica could not
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