19.1.12 problem 12

Internal problem ID [3526]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:40:35 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.270 (sec). Leaf size: 14

DSolve[{(x^2+1)*D[y[x],x]+y[x]^2==-1,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cot \left (\arctan (x)+\frac {\pi }{4}\right ) \]