2.1565   ODE No. 1565

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

(x(ρ2σ2+1)+16x3)y(x)+y(x)(ρ2σ2+8x2)+(x2(ρ2σ2+7)+4x4)y(x)+x4y(4)(x)+6x3y(3)(x)=0 Mathematica : cpu = 0.4196 (sec), leaf count = 242

{{y(x)c1xρ2F3(12ρ2,1ρ2;1ρ,ρ2σ2+1,ρ2+σ2+1;x2)+c3xσ2F3(12σ2,1σ2;1σ,ρ2σ2+1,ρ2σ2+1;x2)+c4xσ2F3(σ2+12,σ2+1;ρ2+σ2+1,ρ2+σ2+1,σ+1;x2)+c2xρ2F3(ρ2+12,ρ2+1;ρ+1,ρ2σ2+1,ρ2+σ2+1;x2)}} Maple : cpu = 0.353 (sec), leaf count = 71

{y(x)=(c1BesselJ(ρ2σ2,x)+c2BesselY(ρ2σ2,x))BesselJ(ρ2+σ2,x)+(c3BesselJ(ρ2σ2,x)+c4BesselY(ρ2σ2,x))BesselY(ρ2+σ2,x)}