Differential Equations/Expert Profile

Abe Mantell

On Vacation
returns 12/25/2016

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!

Experience in the area

Over 15 years teaching at the college level.




B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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    K = Knowledgeability    C = Clarity of Response    P = Politeness
anjali09/12/16101010thank you so much :D
Prashant S Akerkar 07/24/16101010Dear Prof Abe Thanks. Prashant
Peter07/01/16101010Many thanks for your prompt and helpful .....
TIZARD ANSAH09/03/12101010Thank you so much, i could not .....

Recent Answers from Abe Mantell

2016-09-10 differntial equation question:

First solve the associated homogeneous problem: (x^2)y''+xy'+y=0, by letting y=x^n  Substituting that into the DE gives: (x^n)*(n^2+1)=0 ==> n=-i or +i.  Thus, y1=x^i or y2=x^(-i).  Using Euler's formula

2016-06-30 Difficult integral:

Hello Peter,    That certainly is a tough integral!  I see no way to evaluate it in closed form.  Yes, I believe it will have to be done numerically, or express the integrand as a power  series, then you

2016-05-04 ordinary differential equation:

2xydy = 5dy - dx ==> dy/dx = 1/(5-2xy) ==> dx/dy = 5-2xy, which is a 1st order linear ODE  for x as a function of y.    ==> dx/dy + 2yx = 5, integrating factor is u(y)=e^integral(2y dy)=e^(y^2)    ==>

2013-07-26 Laplace transforms - Differential Equations:

Hello Laura,    Let me use IL for "Inverse Laplace"...    So, IL[(9+s)/(4-s^2)] = IL[(7/4)/(s+2)-(11/4*)/(s-2)], by expanding (9+s)/(4-s^2)  using partial fraction decomposition.    Thus, we get (by the

2013-06-24 Vol vs Area:

It makes sense that dV/dr = surface area...    Think about it...if we increase the radius of a sphere by a small amount, say dr,  then the volume increases by about the surface area times the thickness


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