73.7.18 problem 18

Internal problem ID [15097]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 18
Date solved : Thursday, March 13, 2025 at 05:37:50 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

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

\[ y = \frac {4 \left (x +1\right )^{3}}{x^{4}+4 x^{3}+6 x^{2}+4 c_{1} +4 x +1} \]

✓ Mathematica. Time used: 0.202 (sec). Leaf size: 41

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

\begin{align*} y(x)\to \frac {4 (x+1)^3}{x^4+4 x^3+6 x^2+4 x+1+4 c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.277 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {4 \left (x + 1\right )^{3}}{C_{1} + x^{4} + 4 x^{3} + 6 x^{2} + 4 x} \]