6.3.13 problem 14

Internal problem ID [1590]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 04:37:45 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (y-2\right )}{x +1}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 14.555 (sec). Leaf size: 111

ode:=diff(y(x),x)+(y(x)+1)*(y(x)-1)*(y(x)-2)/(1+x) = 0; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\operatorname {RootOf}\left (-2048+\left (x^{6}+6 x^{5}+15 x^{4}+20 x^{3}+15 x^{2}+6 x +257\right ) \textit {\_Z}^{18}+\left (-6 x^{6}-36 x^{5}-90 x^{4}-120 x^{3}-90 x^{2}-36 x -1542\right ) \textit {\_Z}^{12}+\left (9 x^{6}+54 x^{5}+135 x^{4}+180 x^{3}+135 x^{2}+54 x +3081\right ) \textit {\_Z}^{6}\right )}^{6}-1 \]

✓ Mathematica. Time used: 60.57 (sec). Leaf size: 1618

ode=D[y[x],x]+((y[x]+1)*(y[x]-1)*(y[x]-2))/(x+1)==0; 
ic=y[1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out