12.2.41 problem 48(d)

Internal problem ID [1577]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 48(d)
Date solved : Saturday, March 29, 2025 at 11:00:04 PM
CAS classification : [[_homogeneous, `class C`], _rational, _Riccati]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

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

\[ y = -1+\frac {x}{3 \ln \left (x \right )+3 c_1} \]

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \frac {x-3 \log (x)-3 c_1}{3 (\log (x)+c_1)} \\ y(x)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.324 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {8 x^{3}}{3} - 1 \]