x( a2x + y(x)( x2 −y(x)2) ) y′(x)2 −( 2a2xy(x) −( x2 −y(x)2) 2 ) y′(x) + a2y(x)2 −x( x2 −y(x)2) y(x) = 0

4.21.13 $x (a^{2} x + y (x) (x^{2} - y (x)^{2})) y^{'} (x)^{2} - (2 a^{2} x y (x) - {(x^{2} - y (x)^{2})}^{2}) y^{'} (x) + a^{2} y (x)^{2} - x (x^{2} - y (x)^{2}) y (x) = 0$

ODE
$x (a^{2} x + y (x) (x^{2} - y (x)^{2})) y^{'} (x)^{2} - (2 a^{2} x y (x) - {(x^{2} - y (x)^{2})}^{2}) y^{'} (x) + a^{2} y (x)^{2} - x (x^{2} - y (x)^{2}) y (x) = 0$ ODE Classiﬁcation

[_separable]

Book solution method
Change of variable

Mathematica ✓
cpu = 0.135287 (sec), leaf count = 46

${{y (x) \to c_{1} x}, Solve [a^{2} \log (y (x) + x) + x^{2} + y (x)^{2} = a^{2} \log (x - y (x)) + 2 c_{1}, y (x)]}$

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

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4.21.13 x(a2x+y(x)(x2−y(x)2))y′(x)2−(2a2xy(x)−(x2−y(x)2)2)y′(x)+a2y(x)2−x(x2−y(x)2)y(x)=0

4.21.13 $x (a^{2} x + y (x) (x^{2} - y (x)^{2})) y^{'} (x)^{2} - (2 a^{2} x y (x) - {(x^{2} - y (x)^{2})}^{2}) y^{'} (x) + a^{2} y (x)^{2} - x (x^{2} - y (x)^{2}) y (x) = 0$