65.5.3 problem 3

Internal problem ID [15686]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:23:10 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 10

ode:=diff(y(x),x) = 2*sin(x); 
ic:=[y(Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2 \cos \left (x \right )-1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

ode=D[y[x],x]==2*Sin[x]; 
ic={y[Pi]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _{\pi }^x2 \sin (K[1])dK[1]+1 \end{align*}

✓ Sympy. Time used: 0.065 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = - 2 \cos {\left (x \right )} - 1 \]