Internal problem ID [15166]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 304.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {-y^{2}+2 y^{\prime } y x=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve((x-y(x)^2)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y &= \sqrt {-x \left (\ln \left (x \right )-c_{1} \right )} \\ y &= -\sqrt {\left (-\ln \left (x \right )+c_{1} \right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.196 (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*}