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]
\[ \boxed {y^{\prime }+\left (1+2 x \right ) y-x y^{2}=x +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x)=1+x-(1+2*x)*y(x)+x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x +4\right ) {\mathrm e}^{-x}-c_{1}}{\left (2+2 x \right ) {\mathrm e}^{-x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 31
DSolve[y'[x]==1+x-(1+2*x)*y[x]+x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+c_1 e^x+2}{x+c_1 e^x+1} \\ y(x)\to 1 \\ \end{align*}