ODE
\[ \left (x^2-4 y(x)^2\right ) y'(x)^2-4 x^2+6 x y(x) y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.161977 (sec), leaf count = 3017
\[\left \{\left \{y(x)\to -\frac {x}{2}-\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}-\frac {1}{2} \sqrt {-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to \frac {x}{2}+\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}-\frac {1}{2} \sqrt {-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to -\frac {x}{2}-\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}+\frac {1}{2} \sqrt {-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to \frac {x}{2}+\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}+\frac {1}{2} \sqrt {-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to \frac {x}{2}-\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}-\frac {1}{2} \sqrt {\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to -\frac {x}{2}+\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}-\frac {1}{2} \sqrt {\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to \frac {x}{2}-\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}+\frac {1}{2} \sqrt {\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \},\left \{y(x)\to -\frac {x}{2}+\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}+\frac {1}{2} \sqrt {\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}}+2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{9 e^{2 c_1} x^2+\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}}}}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 69
\[ \left \{ -{\frac {3}{4}\ln \left ( {\frac {y \left ( x \right ) -x}{x}} \right ) }-{\frac {1}{4}\ln \left ( {\frac {x+y \left ( x \right ) }{x}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0,-{\frac {1}{4}\ln \left ( {\frac {y \left ( x \right ) -x}{x}} \right ) }-{\frac {3}{4}\ln \left ( {\frac {x+y \left ( x \right ) }{x}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-4*x^2 + y[x]^2 + 6*x*y[x]*y'[x] + (x^2 - 4*y[x]^2)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -x/2 - Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 - Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) - (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> x/2 + Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 - Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) - (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> -x/2 - Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 + Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) - (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> x/2 + Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 + Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) - (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> x/2 - Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 - Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) + (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> -x/2 + Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 - Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) + (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> x/2 - Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 + Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) + (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}, {y[x] -> -x/2 + Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]/2 + Sqrt[2*x^2 - (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) - (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3) + (2*x^3)/Sqrt[x^2 + (2*2^(2/3)*E^(2*C[1]))/(3^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3)) + (2^(1/3)*(9*E^(2*C[1])*x^2 + Sqrt[-48*E^(6*C[1]) + 81*E^(4*C[1])*x^4])^(1/3))/3^(2/3)]]/2}}
Maple raw input
dsolve((x^2-4*y(x)^2)*diff(y(x),x)^2+6*x*y(x)*diff(y(x),x)-4*x^2+y(x)^2 = 0, y(x),'implicit')
Maple raw output
-1/4*ln((y(x)-x)/x)-3/4*ln((x+y(x))/x)-ln(x)-_C1 = 0, -3/4*ln((y(x)-x)/x)-1/4*ln((x+y(x))/x)-ln(x)-_C1 = 0