Internal problem ID [13270]
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: 2.4 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 8
dsolve([(x^2+1)*diff(y(x),x)=1,y(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (x \right )+3 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 9
DSolve[{(x^2+1)*y'[x]==1,{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)+3 \]