57.1.51 problem 51

Internal problem ID [9035]
Book : First order enumerated odes
Section : section 1
Problem number : 51
Date solved : Monday, January 27, 2025 at 05:27:43 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 39

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

\begin{align*} y &= 0 \\ y &= \frac {\left (x +\sqrt {c_{1} x}\right )^{2}}{x} \\ y &= \frac {\left (-x +\sqrt {c_{1} x}\right )^{2}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 46

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