56.1.44 problem 44

Internal problem ID [8756]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 44
Date solved : Monday, January 27, 2025 at 04:48:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 39

dsolve(y(x)=x*(diff(y(x),x))^2,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: 0.052 (sec). Leaf size: 46

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