38.2.7 problem 7

Internal problem ID [6436]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:03:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

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

\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-2 c_1}}{x^{2}}\right ) x \]

✓ Solution by Mathematica

Time used: 2.614 (sec). Leaf size: 25

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

\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}