4.14.32 (a2x+y(x)(x2y(x)2))y(x)+x(x2y(x)2)=a2y(x)

ODE
(a2x+y(x)(x2y(x)2))y(x)+x(x2y(x)2)=a2y(x) ODE Classification

[_rational]

Book solution method
Change of Variable, Two new variables

Mathematica
cpu = 0.126636 (sec), leaf count = 37

Solve[a2log(y(x)+x)+x2+y(x)2=a2log(xy(x))+2c1,y(x)]

Maple
cpu = 0.016 (sec), leaf count = 0 , exception

numeric exception: division by zero

Mathematica raw input

DSolve[x*(x^2 - y[x]^2) + (a^2*x + y[x]*(x^2 - y[x]^2))*y'[x] == a^2*y[x],y[x],x]

Mathematica raw output

Solve[x^2 + a^2*Log[x + y[x]] + y[x]^2 == 2*C[1] + a^2*Log[x - y[x]], y[x]]

Maple raw input

dsolve((a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)+x*(x^2-y(x)^2) = a^2*y(x), y(x),'implicit')

Maple raw output

numeric exception: division by zero