31.1.18 problem 6.5

Internal problem ID [5716]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 6.5
Date solved : Monday, January 27, 2025 at 01:11:19 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 18

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

\[ y(x)\to \arctan (x)+c_1 e^{-\arctan (x)}-1 \]