Internal problem ID [14209]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {1}{x^{2}+1}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 8
dsolve([diff(y(x),x)=1/(1+x^2),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (x \right )+1 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 9
DSolve[{y'[x]==1/(1+x^2),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)+1 \]