30.1.7 problem Example, page 38

Internal problem ID [5695]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 38
Date solved : Monday, January 27, 2025 at 01:07:30 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y \left (x \right ) = -\frac {2 x}{x^{2}-2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 23

DSolve[(y[x]+x*y[x]^2)-x*D[y[x],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*}