Internal problem ID [2571]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 7, page 37
Problem number: 1.a.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2}-y^{2}+y^{\prime } y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (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 \relax (x ) = \sqrt {-2 \ln \relax (x )+c_{1}}\, x \\ y \relax (x ) = -\sqrt {-2 \ln \relax (x )+c_{1}}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 36
DSolve[(x^2-y[x]^2)+x*y[x]*y'[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*}