2.7 problem 7

Internal problem ID [4585]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]

Solve \begin {gather*} \boxed {x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.032 (sec). Leaf size: 25

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

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

Solution by Mathematica

Time used: 24.066 (sec). Leaf size: 25

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

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