8.1.7 problem 7

Internal problem ID [657]
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
Date solved : Monday, January 27, 2025 at 02:56:47 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: 0.029 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 9

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

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