30.1.1 problem Example, page 25

Internal problem ID [5689]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 25
Date solved : Sunday, March 30, 2025 at 10:02:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

ode:=diff(y(x),x) = x*y(x)/(x^2-y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {-\frac {1}{\operatorname {LambertW}\left (-c_1 \,x^{2}\right )}}\, x \]

✓ Mathematica. Time used: 8.295 (sec). Leaf size: 60

ode=D[y[x],x]==x*y[x]/(x^2-y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {i x}{\sqrt {W\left (-e^{-3-2 c_1} x^2\right )}} \\ y(x)\to \frac {i x}{\sqrt {W\left (-e^{-3-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.344 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)/(x**2 - y(x)**2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{C_{1} + \frac {W\left (- x^{2} e^{- 2 C_{1}}\right )}{2}} \]