60.2.235 problem 811

Internal problem ID [10809]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 811
Date solved : Sunday, March 30, 2025 at 07:03:44 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+x y-\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 32

ode:=diff(y(x),x) = (x^3*exp(y(x))+x^4+exp(y(x))*y(x)-exp(y(x))*ln(exp(y(x))+x)+x*y(x)-ln(exp(y(x))+x)*x+x)/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{2}+c_1 x +\ln \left (-\frac {x}{-1+{\mathrm e}^{\frac {x \left (x^{2}+2 c_1 \right )}{2}}}\right ) \]

✓ Mathematica. Time used: 3.068 (sec). Leaf size: 29

ode=D[y[x],x] == (x + E^y[x]*x^3 + x^4 - E^y[x]*Log[E^y[x] + x] - x*Log[E^y[x] + x] + E^y[x]*y[x] + x*y[x])/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\log \left (\frac {-1+e^{-\frac {1}{2} x \left (x^2+2 c_1\right )}}{x}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4 + x**3*exp(y(x)) + x*y(x) - x*log(x + exp(y(x))) + x + y(x)*exp(y(x)) - exp(y(x))*log(x + exp(y(x))))/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**3*(x + exp(y(x))) + x*(y(x) - log(x + exp(y(x))) + 1) + (y(x) - log(x + exp(y(x))))*exp(y(x)))/x**2 cannot be solved by the factorable group method