1.18 problem 6.5

Internal problem ID [3864]

Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 6.5.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y-\arctan \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

\[ y \relax (x ) = \arctan \relax (x )-1+{\mathrm e}^{-\arctan \relax (x )} c_{1} \]

Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 18

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

\begin{align*} y(x)\to \text {ArcTan}(x)+c_1 e^{-\text {ArcTan}(x)}-1 \\ \end{align*}