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
|Giulia||01/10/17||9||9||9||Thank you. I'm studying this EDO in .....|
|anjali||09/12/16||10||10||10||thank you so much :D|
|Prashant S Akerkar||07/24/16||10||10||10||Dear Prof Abe Thanks. Prashant|
|Peter||07/01/16||10||10||10||Many thanks for your prompt and helpful .....|
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
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
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
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
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) ==>