Internal problem ID [3837]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: Example, page 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x y}{x^{2}-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 19
dsolve(diff(y(x),x)=x*y(x)/(x^2-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-\frac {1}{\LambertW \left (-c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 20.741 (sec). Leaf size: 56
DSolve[y'[x]==x*y[x]/(x^2-y[x]^2),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*}