60.2.182 problem 758

Internal problem ID [10756]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 758
Date solved : Friday, March 14, 2025 at 02:28:59 AM
CAS classification : [`x=_G(y,y')`]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 61

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

\[ y = -\frac {6 \operatorname {LambertW}\left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x \right ) {\mathrm e}^{-2 x}}{6}\right )}{-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x} \]

✓ Mathematica. Time used: 0.397 (sec). Leaf size: 86

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

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

✗ Sympy

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

Timed Out