Internal problem ID [11195]
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]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }+y=\arctan \left (x \right )} \]
✓ 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: 0.23 (sec). Leaf size: 18
DSolve[(1+x^2)*y'[x]+y[x]==ArcTan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)+c_1 e^{-\arctan (x)}-1 \]