22.1.72 problem 75

Internal problem ID [4378]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 75
Date solved : Tuesday, September 30, 2025 at 07:23:52 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {2 x +2}{x^{2}+2 c_1 +2 x} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.153 (sec). Leaf size: 15

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

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