29.29.23 problem 845

Internal problem ID [5428]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 845
Date solved : Monday, January 27, 2025 at 11:23:19 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 46

DSolve[x (D[y[x],x])^2==y[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*}