54.2.176 problem 753

Internal problem ID [12050]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 753
Date solved : Sunday, October 12, 2025 at 02:14:53 AM
CAS classification : [`x=_G(y,y')`]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 38

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

\[ y = {\mathrm e}^{-\frac {12 x}{3 x^{4}-4 x^{3}+6 x^{2}+12 \ln \left (x +1\right )-12 c_1 -12 x}} \]

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 102

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

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

✓ Sympy. Time used: 0.885 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = e^{\frac {12 x}{C_{1} - 3 x^{4} + 4 x^{3} - 6 x^{2} + 12 x - 12 \log {\left (x + 1 \right )}}} \]