54.2.126 problem 702

Internal problem ID [12000]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 702
Date solved : Tuesday, September 30, 2025 at 11:52:59 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {-y \,{\mathrm e}^{x}+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (-{\mathrm e}^{x}+x \right ) x} \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 35

ode:=diff(y(x),x) = (-y(x)*exp(x)+x*y(x)-x^3*ln(x)-x^3-x*y(x)^2*ln(x)-x*y(x)^2)/(-exp(x)+x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (\int \frac {x \ln \left (x \right )}{{\mathrm e}^{x}-x}d x +\int \frac {x}{{\mathrm e}^{x}-x}d x +c_1 \right ) x \]

✓ Mathematica. Time used: 0.249 (sec). Leaf size: 53

ode=D[y[x],x] == (-x^3 - x^3*Log[x] - E^x*y[x] + x*y[x] - x*y[x]^2 - x*Log[x]*y[x]^2)/(x*(-E^x + x)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=\int _1^x\frac {K[2] (\log (K[2])+1)}{e^{K[2]}-K[2]}dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-x**3*log(x) - x**3 - x*y(x)**2*log(x) - x*y(x)**2 + x*y(x) - y(x)*exp(x))/(x*(x - exp(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out