60.1.383 problem 392

Internal problem ID [10397]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 392
Date solved : Sunday, March 30, 2025 at 04:36:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} {y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \end{align*}

✓ Maple. Time used: 0.152 (sec). Leaf size: 43

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

\begin{align*} y &= \frac {{\mathrm e}^{\frac {x^{2}}{4}}}{a} \\ y &= \frac {{\mathrm e}^{c_1 \left (-c_1 +x \right )}}{a} \\ y &= \frac {{\mathrm e}^{-c_1 \left (c_1 +x \right )}}{a} \\ \end{align*}

✓ Mathematica. Time used: 0.303 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \frac {e^{\frac {1}{4} c_1 (2 x-c_1)}}{a} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out