Internal problem ID [4372]
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]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }+y=\arctan \left (x \right )} \]
✓ 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)
\[ y \left (x \right ) = \arctan \left (x \right )-1+{\mathrm e}^{-\arctan \left (x \right )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 18
DSolve[(1+x^2)*y'[x]+y[x]==ArcTan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)+c_1 e^{-\arctan (x)}-1 \]