60.2.120 problem 696

Internal problem ID [10694]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 696
Date solved : Sunday, March 30, 2025 at 06:21:56 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x} \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 32

ode:=diff(y(x),x) = (y(x)*ln(x-1)+exp(1+x)*x^3+7*exp(1+x)*x*y(x)^2)/ln(x-1)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\left ({\mathrm e} \int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x +c_1 \right ) \sqrt {7}\right ) x \sqrt {7}}{7} \]

✓ Mathematica. Time used: 0.29 (sec). Leaf size: 52

ode=D[y[x],x] == (E^(1 + x)*x^3 + Log[-1 + x]*y[x] + 7*E^(1 + x)*x*y[x]^2)/(x*Log[-1 + x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{7 K[1]^2+1}dK[1]=\int _1^x\frac {e^{K[2]+1} K[2]}{\log (K[2]-1)}dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**3*exp(x + 1) + 7*x*y(x)**2*exp(x + 1) + y(x)*log(x - 1))/(x*log(x - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(x**2 + 7*y(x)**2)*exp(x + 1) + y(x)*log(x - 1))/(x*log(x - 1)) cannot be solved by the factorable group method