Differential Equations/Expert Profile

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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!

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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Giulia01/10/17Thank you. I'm studying this EDO in .....
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 .....

Recent Answers from Abe Mantell

2017-01-15 Solve for x:

Hello John,    This cannot be solved for analytically in terms of elementary functions.    I did solve it numerically to obtain a very good approximation.  x=-40.7459009034... The attached graph shows

2017-01-09 ODE:

Hello Giulia,    As far as I know, this has no general solution in terms of elementary functions.    A computer algebra system (Maple) gives the following result:  y(x) = KummerM((1/2)*e/b, 1/2, b*(d-x)^2/a^2)*_C2+KummerU((1/2)*e/b

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)    ==>


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