12.5.5 problem 1

Internal problem ID [1629]
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 : 1
Date solved : Monday, January 27, 2025 at 05:15:15 AM
CAS classification : [_quadrature]

\begin{align*} y+y^{\prime }&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

\[ y = \frac {1}{1+{\mathrm e}^{x} c_1} \]

✓ Solution by Mathematica

Time used: 0.694 (sec). Leaf size: 54

DSolve[D[y[x],x]+y[x]==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {1+e^{2 (x+c_1)}}} \\ y(x)\to \frac {1}{\sqrt {1+e^{2 (x+c_1)}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}