Internal problem ID [15155]
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: 293.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-y^{\prime } y x=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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 &= \sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ y &= -\sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.159 (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*}