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
|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 .....|
|TIZARD ANSAH||09/03/12||10||10||10||Thank you so much, i could not .....|
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) ==>
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
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