54.2.190 problem 767

Internal problem ID [12064]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 767
Date solved : Wednesday, October 01, 2025 at 12:08:54 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 26

ode:=diff(y(x),x) = (-8*x*y(x)-x^3+2*x^2-8*x+32)/(32*y(x)+4*x^2-8*x+32); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x^{2}}{8}+4 \operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{-\frac {3}{4}-\frac {x}{16}}}{4}\right )+\frac {x}{4}+3 \]

✓ Mathematica. Time used: 0.725 (sec). Leaf size: 53

ode=D[y[x],x] == (32 - 8*x + 2*x^2 - x^3 - 8*x*y[x])/(32 - 8*x + 4*x^2 + 32*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 W\left (-e^{-\frac {x}{16}-1+c_1}\right )-\frac {x^2}{8}+\frac {x}{4}+3\\ y(x)&\to -\frac {x^2}{8}+\frac {x}{4}+3 \end{align*}

✓ Sympy. Time used: 60.566 (sec). Leaf size: 707

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-x**3 + 2*x**2 - 8*x*y(x) - 8*x + 32)/(4*x**2 - 8*x + 32*y(x) + 32),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]