# Differential Equations/Expert Profile

## Abe Mantell

On Vacation
returns 12/25/2016
##### Expertise

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.

##### Organizations

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

##### Education/Credentials

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

### Recent Reviews from Users

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
Bob01/23/14101010
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

Differential Equations