Internal problem ID [6614]
Book: First order enumerated odes
Section: section 1
Problem number: 51.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.186 (sec). Leaf size: 39
dsolve(diff(y(x),x)^2=y(x)/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (x +\sqrt {c_{1} x}\right )^{2}}{x} \\ y \relax (x ) = \frac {\left (-x +\sqrt {c_{1} x}\right )^{2}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 46
DSolve[(y'[x])^2==y[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 \sqrt {x}+c_1\right ){}^2 \\ y(x)\to \frac {1}{4} \left (2 \sqrt {x}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}