Internal problem ID [7371]
Book: First order enumerated odes
Section: section 1
Problem number: 55.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}-\frac {1}{y x}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 51
dsolve(diff(y(x),x)^2=1/(y(x)*x),y(x), singsol=all)
\begin{align*} \frac {y \left (x \right ) \sqrt {x y \left (x \right )}-c_{1} \sqrt {x}-3 x}{\sqrt {x}} &= 0 \\ \frac {y \left (x \right ) \sqrt {x y \left (x \right )}-c_{1} \sqrt {x}+3 x}{\sqrt {x}} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.748 (sec). Leaf size: 53
DSolve[(y'[x])^2==1/(y[x]*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-2 \sqrt {x}+c_1\right ){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (2 \sqrt {x}+c_1\right ){}^{2/3} \\ \end{align*}