ODE
\[ y(x)^5 \left (-y'(x)\right )+3 x y(x)^4 y'(x)^2+1=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.656617 (sec), leaf count = 97
\[\left \{\left \{y(x)\to -\sqrt [3]{-\frac {1}{2}} e^{-\frac {c_1}{6}} \sqrt [3]{12 x+e^{c_1}}\right \},\left \{y(x)\to e^{-\frac {c_1}{6}} \sqrt [3]{6 x+\frac {e^{c_1}}{2}}\right \},\left \{y(x)\to (-1)^{2/3} e^{-\frac {c_1}{6}} \sqrt [3]{6 x+\frac {e^{c_1}}{2}}\right \}\right \}\]
Maple ✓
cpu = 1.959 (sec), leaf count = 295
\[\left [y \left (x \right ) = 12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = -12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = \left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = \left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 12^{\frac {1}{6}} x^{\frac {1}{6}}, y \left (x \right ) = \frac {3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = -\frac {3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) 3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) 3^{\frac {1}{6}} \left (-\left (\textit {\_C1}^{2}-2 x \textit {\_C1} +x^{2}\right ) \textit {\_C1}^{5}\right )^{\frac {1}{6}}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[1 - y[x]^5*y'[x] + 3*x*y[x]^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(((-1/2)^(1/3)*(E^C[1] + 12*x)^(1/3))/E^(C[1]/6))}, {y[x] -> (E^C[1]/2 + 6*x)^(1/3)/E^(C[1]/6)}, {y[x] -> ((-1)^(2/3)*(E^C[1]/2 + 6*x)^(1/3))/E^(C[1]/6)}}
Maple raw input
dsolve(3*x*y(x)^4*diff(y(x),x)^2-y(x)^5*diff(y(x),x)+1 = 0, y(x))
Maple raw output
[y(x) = 12^(1/6)*x^(1/6), y(x) = -12^(1/6)*x^(1/6), y(x) = (-1/2-1/2*I*3^(1/2))*12^(1/6)*x^(1/6), y(x) = (-1/2+1/2*I*3^(1/2))*12^(1/6)*x^(1/6), y(x) = (1/2-1/2*I*3^(1/2))*12^(1/6)*x^(1/6), y(x) = (1/2+1/2*I*3^(1/2))*12^(1/6)*x^(1/6), y(x) = 3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = -3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (-1/2-1/2*I*3^(1/2))*3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (-1/2+1/2*I*3^(1/2))*3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (1/2-1/2*I*3^(1/2))*3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6), y(x) = (1/2+1/2*I*3^(1/2))*3^(1/6)/_C1*(-(_C1^2-2*_C1*x+x^2)*_C1^5)^(1/6)]