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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x y+\left (y^{2}-x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 19
dsolve(x*y(x)+(y(x)^2-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-\frac {1}{\LambertW \left (-c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 20.283 (sec). Leaf size: 56
DSolve[x*y[x]+(y[x]^2-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i x}{\sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^2\right )}} \\ y(x)\to \frac {i x}{\sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}