54.2.90 problem 666

Internal problem ID [11964]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 666
Date solved : Tuesday, September 30, 2025 at 11:49:35 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.135 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to e^{x^3-2 x^2+4 x-c_1 e^{-x}-3} \end{align*}

✓ Sympy. Time used: 1.199 (sec). Leaf size: 22

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

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