Internal problem ID [5279]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 25 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {-y^{2}+2 x y y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve((x-y(x)^2)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {-\ln \left (x \right ) x +c_{1} x} y = -\sqrt {-\ln \left (x \right ) x +c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 44
DSolve[(x-y[x]^2)+2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {-\log (x)+c_1} y(x)\to \sqrt {x} \sqrt {-\log (x)+c_1} \end{align*}