56.1.34 problem 35

Internal problem ID [8746]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 35
Date solved : Monday, January 27, 2025 at 04:46:14 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 36

dsolve((y(x)^2+2/x)+2*y(x)*x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 44

DSolve[(y[x]^2+2/x)+2*y[x]*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-2 \log (x)+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {-2 \log (x)+c_1}}{\sqrt {x}} \\ \end{align*}