60.2.188 problem 764

Internal problem ID [10762]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 764
Date solved : Sunday, March 30, 2025 at 06:35:29 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 70

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

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

✓ Sympy. Time used: 1.229 (sec). Leaf size: 36

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

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