2.1500   ODE No. 1500

ν(2x+1)y(x)ν(x+1)y(x)x(v+x)y(x)+x2y(3)(x)=0

Mathematica : cpu = 29.874 (sec), leaf count = 0

DSolve[-(nu*(1 + x)*y[x]) + nu*(1 + 2*x)*Derivative[1][y][x] - x*(v + x)*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
 

, DifferentialRoot result

{{y(x)(x)}}

Maple : cpu = 0.201 (sec), leaf count = 55

dsolve(x^2*diff(diff(diff(y(x),x),x),x)-(x+nu)*x*diff(diff(y(x),x),x)+nu*(2*x+1)*diff(y(x),x)-nu*(1+x)*y(x)=0,y(x))
 
y(x)=c1ex+c2xν2+12BesselJ(ν1,2νx)+c3xν2+12BesselY(ν1,2νx)