Internal problem ID [15079]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 191.
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: 0.0 (sec). Leaf size: 25
dsolve(( x+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {\left (c_{1} +\ln \left (x \right )\right ) x} \\ y \left (x \right ) &= -\sqrt {\left (c_{1} +\ln \left (x \right )\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 40
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*}