ODE
\[ x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2-\left (2 a^2 x y(x)-\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0 \] ODE Classification
[_separable]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.135287 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 x\right \},\text {Solve}\left [a^2 \log (y(x)+x)+x^2+y(x)^2=a^2 \log (x-y(x))+2 c_1,y(x)\right ]\right \}\]
Maple ✗
cpu = 24.846 (sec), leaf count = 0 , exception
numeric exception: division by zero
Mathematica raw input
DSolve[a^2*y[x]^2 - x*y[x]*(x^2 - y[x]^2) - (2*a^2*x*y[x] - (x^2 - y[x]^2)^2)*y'[x] + x*(a^2*x + y[x]*(x^2 - y[x]^2))*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1]}, 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(x*(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)^2-(2*a^2*x*y(x)-(x^2-y(x)^2)^2)*diff(y(x),x)+a^2*y(x)^2-x*y(x)*(x^2-y(x)^2) = 0, y(x),'implicit')
Maple raw output
numeric exception: division by zero