57.1.55 problem 55

Internal problem ID [9039]
Book : First order enumerated odes
Section : section 1
Problem number : 55
Date solved : Monday, January 27, 2025 at 05:27:51 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}&=\frac {1}{y x} \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 51

dsolve(diff(y(x),x)^2=1/(y(x)*x),y(x), singsol=all)
 

\begin{align*} \frac {y \sqrt {x y}-\sqrt {x}\, c_{1} -3 x}{\sqrt {x}} &= 0 \\ \frac {y \sqrt {x y}-\sqrt {x}\, c_{1} +3 x}{\sqrt {x}} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.346 (sec). Leaf size: 53

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