Internal problem ID [15120]
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: 234.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Riccati]
\[ \boxed {x y^{\prime }-y^{2}+\left (2 x +1\right ) y=x^{2}+2 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x*diff(y(x),x)-y(x)^2+(2*x+1)*y(x)=x^2+2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{2}-x -1}{c_{1} x -1} \]
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 34
DSolve[x*y'[x]-y[x]^2+(2*x+1)*y[x]==x^2+2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2-c_1 x-c_1}{x-c_1} \\ y(x)\to x+1 \\ \end{align*}