Internal problem ID [36]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-\left (1+y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((x^2+1)*diff(y(x),x) = (1+y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\arctan \relax (x )+c_{1}+1}{\arctan \relax (x )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 21
DSolve[(x^2+1)*y'[x]== (1+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-\frac {1}{\text {ArcTan}(x)+c_1} \\ y(x)\to -1 \\ \end{align*}