8.3.10 problem 10

Internal problem ID [686]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:57:57 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 25

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

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