88.8.3 problem 3

Internal problem ID [24011]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:54:03 PM
CAS classification : [_linear]

\begin{align*} x^{3}+2 y+\left (1+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 22

ode:=x^3+2*y(x)+(1+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\frac {1}{5} x^{5}-\frac {1}{4} x^{4}+c_1}{\left (x +1\right )^{2}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 29

ode=( x^3+2*y[x] )+( x+1 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-4 x^5-5 x^4+20 c_1}{20 (x+1)^2} \end{align*}

✓ Sympy. Time used: 0.166 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {C_{1} - \frac {x^{5}}{5} - \frac {x^{4}}{4}}{x^{2} + 2 x + 1} \]