54.2.379 problem 958

Internal problem ID [12253]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 958
Date solved : Wednesday, October 01, 2025 at 01:23:37 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 40

ode:=diff(y(x),x) = 1/(2*x+1)*(2*x+4*y(x)*ln(2*x+1)*x+6*y(x)^2*ln(2*x+1)*x+6*y(x)*ln(2*x+1)^2*x+2*ln(2*x+1)^3*x+2*x*y(x)^3+2*ln(2*x+1)^2*x+2*x*y(x)^2-1+3*y(x)^2*ln(2*x+1)+3*y(x)*ln(2*x+1)^2+y(x)^2+y(x)^3+2*y(x)*ln(2*x+1)+ln(2*x+1)^2+ln(2*x+1)^3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (2 x +1\right )-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +x +3 c_1 \right )}{9} \]

✓ Mathematica. Time used: 0.218 (sec). Leaf size: 60

ode=D[y[x],x] == (-1 + 2*x + Log[1 + 2*x]^2 + 2*x*Log[1 + 2*x]^2 + Log[1 + 2*x]^3 + 2*x*Log[1 + 2*x]^3 + 2*Log[1 + 2*x]*y[x] + 4*x*Log[1 + 2*x]*y[x] + 3*Log[1 + 2*x]^2*y[x] + 6*x*Log[1 + 2*x]^2*y[x] + y[x]^2 + 2*x*y[x]^2 + 3*Log[1 + 2*x]*y[x]^2 + 6*x*Log[1 + 2*x]*y[x]^2 + y[x]^3 + 2*x*y[x]^3)/(1 + 2*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 \log (2 x+1)+3 y(x)+1}{\sqrt [3]{29}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x*y(x)**3 + 6*x*y(x)**2*log(2*x + 1) + 2*x*y(x)**2 + 6*x*y(x)*log(2*x + 1)**2 + 4*x*y(x)*log(2*x + 1) + 2*x*log(2*x + 1)**3 + 2*x*log(2*x + 1)**2 + 2*x + y(x)**3 + 3*y(x)**2*log(2*x + 1) + y(x)**2 + 3*y(x)*log(2*x + 1)**2 + 2*y(x)*log(2*x + 1) + log(2*x + 1)**3 + log(2*x + 1)**2 - 1)/(2*x + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out