Differential Equations/Expert Profile

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Recent Answers from Dr. Nyayapati Swami

2012-04-24 Matrices and Determinants Elements:

Yes, the elements can be any real or complex numbers. In fact, one can consider matrices with elements from any Field. (In mathematics, a field is an algebraic structure more general than real or complex

2012-03-18 F/U to my Maximum Principle question...:

Hi Joe,  I am not an expert in this area (Pdes) that is why I rejected your question. If you still insist, then let me give you my view:    The way the maximum principle works is first show that the maximum

2011-07-29 Power series solution for differential equation:

Replacing x by x+1 changes to eqn to  dy/dx = 2/(x+1) + 3 - (x + 1)^2   [note dy/d(x+1) = dy/dx)    Expand  2/(x+1) into a power series (powers of x):  2/(x+1) = 2 (1 - x + x^2 - x^3 + .... )  (x + 1)^2

2011-03-04 Autonomous Nonlinear System of ODE:

x^3=2y^3=2(2x^3)=4x^3  x^3 - 4x^3 = 0  -3x^3=0  x=0  So x=0, y=0 is the only critical point of the system.  If you want to study further, you can find particular solutions:    The function y(t) = 0 satisfies

2011-02-28 concave functions:

A function f(x) is concave if its second-order derivative f''(x) is negative.  In your example, y = a x^b, therefore   dy/dx = abx^(b-1) and  the second derivative is  d^2y/dx^2 = a b (b-1) x^(b-2)  Since