60.2.134 problem 710

Internal problem ID [10708]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 710
Date solved : Wednesday, March 05, 2025 at 12:22:53 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 30

ode:=diff(y(x),x) = (-ln(x)+exp(1/x)+4*x^2*y(x)+2*x+2*x*y(x)^2+2*x^3)/(ln(x)-exp(1/x)); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 1.061 (sec). Leaf size: 38

ode=D[y[x],x] == (E^x^(-1) + 2*x + 2*x^3 - Log[x] + 4*x^2*y[x] + 2*x*y[x]^2)/(-E^x^(-1) + Log[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x+\tan \left (\int _1^x-\frac {2 K[5]}{e^{\frac {1}{K[5]}}-\log (K[5])}dK[5]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x**3 + 4*x**2*y(x) + 2*x*y(x)**2 + 2*x + exp(1/x) - log(x))/(-exp(1/x) + log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : Index out of range: a[1]