ODE
\[ -a+y(x)^3 \left (-y'(x)\right )+2 x y(x)^2 y'(x)^2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.588598 (sec), leaf count = 64
\[\left \{\left \{y(x)\to -\frac {e^{-\frac {c_1}{4}} \sqrt {-8 a x+e^{c_1}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {e^{-\frac {c_1}{4}} \sqrt {-8 a x+e^{c_1}}}{\sqrt {2}}\right \}\right \}\]
Maple ✓
cpu = 2.163 (sec), leaf count = 175
\[\left [y \left (x \right ) = 2^{\frac {3}{4}} \left (-a x \right )^{\frac {1}{4}}, y \left (x \right ) = -2^{\frac {3}{4}} \left (-a x \right )^{\frac {1}{4}}, y \left (x \right ) = -i 2^{\frac {3}{4}} \left (-a x \right )^{\frac {1}{4}}, y \left (x \right ) = i 2^{\frac {3}{4}} \left (-a x \right )^{\frac {1}{4}}, y \left (x \right ) = \frac {2^{\frac {1}{4}} \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{3}\right )^{\frac {1}{4}}}{\textit {\_C1}}, y \left (x \right ) = -\frac {2^{\frac {1}{4}} \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{3}\right )^{\frac {1}{4}}}{\textit {\_C1}}, y \left (x \right ) = -\frac {i 2^{\frac {1}{4}} \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{3}\right )^{\frac {1}{4}}}{\textit {\_C1}}, y \left (x \right ) = \frac {i 2^{\frac {1}{4}} \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{3}\right )^{\frac {1}{4}}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-a - y[x]^3*y'[x] + 2*x*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[E^C[1] - 8*a*x]/(Sqrt[2]*E^(C[1]/4)))}, {y[x] -> Sqrt[E^C[1] - 8*a*x]/(Sqrt[2]*E^(C[1]/4))}}
Maple raw input
dsolve(2*x*y(x)^2*diff(y(x),x)^2-y(x)^3*diff(y(x),x)-a = 0, y(x))
Maple raw output
[y(x) = 2^(3/4)*(-a*x)^(1/4), y(x) = -2^(3/4)*(-a*x)^(1/4), y(x) = -I*2^(3/4)*(-a*x)^(1/4), y(x) = I*2^(3/4)*(-a*x)^(1/4), y(x) = 1/_C1*2^(1/4)*(a*(_C1^2-2*_C1*x+x^2)*_C1^3)^(1/4), y(x) = -1/_C1*2^(1/4)*(a*(_C1^2-2*_C1*x+x^2)*_C1^3)^(1/4), y(x) = -I/_C1*2^(1/4)*(a*(_C1^2-2*_C1*x+x^2)*_C1^3)^(1/4), y(x) = I/_C1*2^(1/4)*(a*(_C1^2-2*_C1*x+x^2)*_C1^3)^(1/4)]