Internal problem ID [5093]
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`]]
\[ \boxed {y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-2 c_{1}}}{x^{2}}\right )-2 c_{1}}}{x} \]
✓ Solution by Mathematica
Time used: 2.801 (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 W\left (-\frac {e^{-c_1}}{x^2}\right ) y(x)\to 0 \end{align*}