ODE
\[ -a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.686863 (sec), leaf count = 102
\[\left \{\left \{y(x)\to -\sqrt [3]{-\frac {1}{2}} e^{-\frac {c_1}{6}} \sqrt [3]{-4 a x+e^{c_1}}\right \},\left \{y(x)\to \frac {e^{-\frac {c_1}{6}} \sqrt [3]{-4 a x+e^{c_1}}}{\sqrt [3]{2}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} e^{-\frac {c_1}{6}} \sqrt [3]{-4 a x+e^{c_1}}}{\sqrt [3]{2}}\right \}\right \}\]
Maple ✓
cpu = 2.134 (sec), leaf count = 295
\[\left [y \left (x \right ) = 2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = -2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 2^{\frac {1}{3}} \left (-a x \right )^{\frac {1}{6}}, y \left (x \right ) = \frac {\left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = -\frac {\left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (a \left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-a - 3*y[x]^5*y'[x] + 9*x*y[x]^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(((-1/2)^(1/3)*(E^C[1] - 4*a*x)^(1/3))/E^(C[1]/6))}, {y[x] -> (E^C[1] - 4*a*x)^(1/3)/(2^(1/3)*E^(C[1]/6))}, {y[x] -> ((-1)^(2/3)*(E^C[1] - 4*a*x)^(1/3))/(2^(1/3)*E^(C[1]/6))}}
Maple raw input
dsolve(9*x*y(x)^4*diff(y(x),x)^2-3*y(x)^5*diff(y(x),x)-a = 0, y(x))
Maple raw output
[y(x) = 2^(1/3)*(-a*x)^(1/6), y(x) = -2^(1/3)*(-a*x)^(1/6), y(x) = (-1/2-1/2*I*3^(1/2))*2^(1/3)*(-a*x)^(1/6), y(x) = (-1/2+1/2*I*3^(1/2))*2^(1/3)*(-a*x)^(1/6), y(x) = (1/2-1/2*I*3^(1/2))*2^(1/3)*(-a*x)^(1/6), y(x) = (1/2+1/2*I*3^(1/2))*2^(1/3)*(-a*x)^(1/6), y(x) = 1/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = -1/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (-1/2-1/2*I*3^(1/2))/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (-1/2+1/2*I*3^(1/2))/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (1/2-1/2*I*3^(1/2))/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (1/2+1/2*I*3^(1/2))/_C1*(a*(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6)]