75.10.3 problem 234

Internal problem ID [16850]
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
Date solved : Tuesday, January 28, 2025 at 09:34:55 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Riccati]

\begin{align*} x y^{\prime }-y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \end{align*}

✓ Solution by Maple

Time used: 0.062 (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)
 

\[ y = \frac {c_{1} x^{2}-x -1}{c_{1} x -1} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 34

DSolve[x*D[y[x],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*}