MATH−WHIZZKID
using kamke find the genral
solution for the differential equation
1. x^2 y′′+x^2 y′−2y=0
−−−−−−−−−
solve this using forbenius mtd
1.x^2 y′′+(x^3 −3x)y′+(4−2x)y=0
−−−−−−−−
solve the differential eqn by power series
1. y′′−2xy′+2py=0
−−−−−−−−−
use perseval′s theorem to
∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx.
−−−−−−−−−−
evaluate this integral by contour integration
1. ∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx.
−−−−−−−−−
∮_c ((1+e^(i𝛑z) )/((z−1)^2 (z+1)^2 ))dz
c−upper half plane
klipto−quanta⊎