60.1.407 problem 418

Internal problem ID [10421]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 418
Date solved : Sunday, March 30, 2025 at 04:41:23 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a y&=0 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 42

ode:=x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= -\frac {x \left (\operatorname {LambertW}\left (-\frac {x \,{\mathrm e}}{c_1 a}\right )-1\right )^{2} a}{\operatorname {LambertW}\left (-\frac {x \,{\mathrm e}}{c_1 a}\right )} \\ \end{align*}

✓ Mathematica. Time used: 2.121 (sec). Leaf size: 173

ode=a*y[x] - y[x]*D[y[x],x] + x*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solve}\left [\text {arctanh}\left (\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}}}\right )+\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}-4 a}-\sqrt {\frac {y(x)}{x}}}&=\frac {\log (x)}{2}+c_1,y(x)\right ] \\ \text {Solve}\left [\text {arctanh}\left (\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}}}\right )-\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}}&=-\frac {\log (x)}{2}+c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded