Internal problem ID [4275]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve((y(x)^2-x*y(x))+(x^2+x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{\operatorname {LambertW}\left (c_{1} x^{2}\right )} \]
✓ Solution by Mathematica
Time used: 4.294 (sec). Leaf size: 25
DSolve[(y[x]^2-x*y[x])+(x^2+x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{W\left (e^{-c_1} x^2\right )} \\ y(x)\to 0 \\ \end{align*}