26.1.1 problem 1.a

Internal problem ID [4241]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.a
Date solved : Monday, January 27, 2025 at 08:43:45 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 36

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

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