Internal problem ID [15010]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {x^{2} y^{\prime }-y^{2}+y x=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)=y(x)^2-x*y(x)+x^2,y(x), singsol=all)
\[ y = \frac {x \left (\ln \left (x \right )+c_{1} -1\right )}{\ln \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 25
DSolve[x^2*y'[x]==y[x]^2-x*y[x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (\log (x)-1+c_1)}{\log (x)+c_1} \\ y(x)\to x \\ \end{align*}