15.1.13 problem 13

Internal problem ID [2853]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 13
Date solved : Monday, January 27, 2025 at 06:20:00 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 25

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

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