55.1.2 problem HW 1 problem 6(b)

Internal problem ID [8698]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : HW 1 problem 6(b)
Date solved : Monday, January 27, 2025 at 04:19:31 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

Solution by Maple

Time used: 0.049 (sec). Leaf size: 15

dsolve([(x^2+1)*diff(y(x),x)+y(x)^2=-1,y(0) = 1],y(x), singsol=all)
 
\[ y = \frac {1-x}{x +1} \]

Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 14

DSolve[{(x^2+1)*D[y[x],x]+y[x]^2==-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \cot \left (\arctan (x)+\frac {\pi }{4}\right ) \]