7.3.10 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 : Friday, February 07, 2025 at 08:13:12 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.230 (sec). Leaf size: 30

DSolve[(1+x)^2*D[y[x],x]==(1+y[x])^2,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*}