7.1.7 problem 7

Internal problem ID [7]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 7
Date solved : Friday, February 07, 2025 at 08:11:46 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 8

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

\[ y = 10 \arctan \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 9

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

\[ y(x)\to 10 \arctan (x) \]