54.2.129 problem 705

Internal problem ID [12003]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 705
Date solved : Tuesday, September 30, 2025 at 11:53:10 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 +x^{3}+x^{4}\right ) y}{x} \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 23

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

\[ y = x^{x} {\mathrm e}^{c_1 x +\frac {1}{2} x^{3}+\frac {1}{3} x^{4}} \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to x^x e^{\frac {1}{6} x \left (2 x^3+3 x^2+3+6 c_1\right )} \end{align*}

✓ Sympy. Time used: 0.654 (sec). Leaf size: 26

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

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