Internal problem ID [10171]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 16.
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: 0.066 (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*}