12.5.1 problem Example 1

Internal problem ID [1625]
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 : Example 1
Date solved : Monday, January 27, 2025 at 05:14:56 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 27

DSolve[D[y[x],x]-y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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