2.1170   ODE No. 1170

y(x)(ax2+b)+x2y(x)+2xy(x)=0

Mathematica : cpu = 0.0123349 (sec), leaf count = 58

DSolve[(b + a*x^2)*y[x] + 2*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 
{{y(x)c1j12(14b1)(ax)+c2y12(14b1)(ax)}}

Maple : cpu = 0.059 (sec), leaf count = 43

dsolve(x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)+(a*x^2+b)*y(x)=0,y(x))
 
y(x)=c2BesselY(14b2,ax)+c1BesselJ(14b2,ax)x