60.1.260 problem 261

Internal problem ID [10274]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 261
Date solved : Monday, January 27, 2025 at 06:42:56 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.164 (sec). Leaf size: 64

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

\[ \text {Solve}\left [\int _1^{-\frac {4 x y(x)+1}{\sqrt [3]{2} (2 x y(x)-1)}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]+\frac {2}{9} 2^{2/3} \log (x)=c_1,y(x)\right ] \]