Internal problem ID [1029]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-1-x +\left (1+2 x \right ) y-x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
dsolve(diff(y(x),x)=1+x-(1+2*x)*y(x)+x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {2 \,{\mathrm e}^{-x}}{c_{1}-2 \left (x +1\right ) {\mathrm e}^{-x}} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 23
DSolve[y'[x]==1+x-(1+2*x)*y[x]+x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {1}{x+c_1 e^x+1} \\ y(x)\to 1 \\ \end{align*}