ODE
\[ \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x) \] ODE Classification
[_rational]
Book solution method
Change of Variable, Two new variables
Mathematica ✓
cpu = 0.711458 (sec), leaf count = 37
\[\text {Solve}\left [a^2 \log (y(x)+x)+x^2+y(x)^2=a^2 \log (x-y(x))+2 c_1,y(x)\right ]\]
Maple ✗
cpu = 0. (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))
Maple raw output
\verbnumeric exception: division by zero||