62.5.3 problem Ex 3

Internal problem ID [12818]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 12. Page 18
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:24:43 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 63

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

\[ \text {Solve}\left [\int _1^{-\frac {2 x y(x)+1}{\sqrt [3]{2} (x y(x)-1)}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]+\frac {2}{9} 2^{2/3} \log (x)=c_1,y(x)\right ] \]