60.1.405 problem 407

Internal problem ID [10419]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 407
Date solved : Monday, January 27, 2025 at 07:42:57 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}-y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x*diff(y(x),x)^2-y(x) = 0,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: 0.051 (sec). Leaf size: 46

DSolve[-y[x] + x*D[y[x],x]^2==0,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*}