1.3.10 problem 10

Internal problem ID [50]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 03:40:49 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 17

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

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