12.5.55 problem 56

Internal problem ID [1679]
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
Date solved : Monday, January 27, 2025 at 05:25:18 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

dsolve(diff(y(x),x)=1+x-(1+2*x)*y(x)+x*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {\left (2 x +4\right ) {\mathrm e}^{-x}-c_1}{\left (2 x +2\right ) {\mathrm e}^{-x}-c_1} \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 31

DSolve[D[y[x],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*}