Internal problem ID [15121]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 9. The Riccati equation. Exercises page 75
Problem number: 235.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]
\[ \boxed {x^{2} y^{\prime }-y^{2} x^{2}-y x=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x)=x^2*y(x)^2+x*y(x)+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\ln \left (x \right )+c_{1} -1}{x \left (-c_{1} +\ln \left (x \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 33
DSolve[x^2*y'[x]==x^2*y[x]^2+x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\log (x)+1+c_1}{x \log (x)+c_1 x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}