Internal problem ID [12961]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 2. Integration and differential equations. Additional exercises. page
32
Problem number: 2.7 c.
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 (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(y(x),x)=1/(x^2+1),y(1) = 0],y(x), singsol=all)
\[ y = \arctan \left (x \right )-\frac {\pi }{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 13
DSolve[{y'[x]==1/(x^2+1),{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)-\frac {\pi }{4} \]