Internal problem ID [7370]
Book: First order enumerated odes
Section: section 1
Problem number: 54.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {{y^{\prime }}^{3}-\frac {y^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 353
dsolve(diff(y(x),x)^3=y(x)^2/x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {3 x^{\frac {4}{3}} c_{1}}{8}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{8}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{16}+\frac {3 c_{1} \left (1-i \sqrt {3}\right ) x^{\frac {4}{3}}}{16}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{16}+\frac {3 \left (1+i \sqrt {3}\right ) c_{1} x^{\frac {4}{3}}}{16}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 x^{\frac {4}{3}} c_{1}}{16}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 \left (i \sqrt {3}-1\right ) c_{1} x^{\frac {4}{3}}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 c_{1} \left (-i \sqrt {3}-1\right ) x^{\frac {4}{3}}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= -\frac {3 x^{\frac {4}{3}} c_{1}}{16}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 c_{1} \left (1-i \sqrt {3}\right ) x^{\frac {4}{3}}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 \left (1+i \sqrt {3}\right ) c_{1} x^{\frac {4}{3}}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 152
DSolve[(y'[x])^3==y[x]^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{216} \left (3 x^{2/3}+2 c_1\right ){}^3 \\ y(x)\to \frac {1}{216} \left (18 i \left (\sqrt {3}+i\right ) c_1{}^2 x^{2/3}-27 i \left (\sqrt {3}-i\right ) c_1 x^{4/3}+27 x^2+8 c_1{}^3\right ) \\ y(x)\to \frac {1}{216} \left (-18 i \left (\sqrt {3}-i\right ) c_1{}^2 x^{2/3}+27 i \left (\sqrt {3}+i\right ) c_1 x^{4/3}+27 x^2+8 c_1{}^3\right ) \\ y(x)\to 0 \\ \end{align*}