60.1.101 problem 101

Internal problem ID [10115]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 101
Date solved : Monday, January 27, 2025 at 06:28:01 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+x y^{2}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(x*diff(y(x),x) + x*y(x)^2 - y(x)=0,y(x), singsol=all)
 

\[ y = \frac {2 x}{x^{2}+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 23

DSolve[x*D[y[x],x] + x*y[x]^2 - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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