Internal problem ID [2124]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations.
page 43
Problem number: Problem 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y^{2}+1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 11
dsolve([(x^2+1)*diff(y(x),x)+y(x)^2=-1,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \cot \left (\arctan \relax (x )+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 14
DSolve[{(x^2+1)*y'[x]+y[x]^2==-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot \left (\text {ArcTan}(x)+\frac {\pi }{4}\right ) \\ \end{align*}