89.5.2 problem 2

Internal problem ID [24352]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:21:36 PM
CAS classification : [_linear]

\begin{align*} 3 y x +3 y-4+\left (1+x \right )^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=3*x*y(x)+3*y(x)-4+(1+x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x^{2}+c_1 +4 x}{\left (x +1\right )^{3}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 22

ode=(3*x*y[x]+3*y[x]-4)+( x+1 )^2*D[y[x],x]== 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x^2+4 x+c_1}{(x+1)^3} \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*y(x) + (x + 1)**2*Derivative(y(x), x) + 3*y(x) - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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