57.1.52 problem 52

Internal problem ID [9036]
Book : First order enumerated odes
Section : section 1
Problem number : 52
Date solved : Monday, January 27, 2025 at 05:27:45 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2}&=\frac {y^{2}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 27

dsolve(diff(y(x),x)^2=y(x)^2/x,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= c_{1} {\mathrm e}^{-2 \sqrt {x}} \\ y &= c_{1} {\mathrm e}^{2 \sqrt {x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 38

DSolve[(D[y[x],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*}