1.7 problem 7

Internal problem ID [7]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.2. Integrals as general and particular solutions. Page 16
Problem number: 7.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {10}{x^{2}+1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 8

dsolve([diff(y(x),x) = 10/(x^2+1),y(0) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = 10 \arctan \relax (x ) \]

Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 9

DSolve[{y'[x]==10/(x^2+1),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 10 \text {ArcTan}(x) \\ \end{align*}