Internal problem ID [6615]
Book: First order enumerated odes
Section: section 1
Problem number: 52.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.196 (sec). Leaf size: 27
dsolve(diff(y(x),x)^2=y(x)^2/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = c_{1} {\mathrm e}^{-2 \sqrt {x}} \\ y \relax (x ) = c_{1} {\mathrm e}^{2 \sqrt {x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 38
DSolve[(y'[x])^2==y[x]^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-2 \sqrt {x}} \\ y(x)\to c_1 e^{2 \sqrt {x}} \\ y(x)\to 0 \\ \end{align*}