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 : Tuesday, March 04, 2025 at 11:31:02 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*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 8

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

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

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

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

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 10/(x**2 + 1),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 10 \operatorname {atan}{\left (x \right )} \]