71.5.4 problem 4

Internal problem ID [14321]
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 : 4
Date solved : Wednesday, March 05, 2025 at 10:45:43 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

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

\[ y(x)\to \int _{\frac {\pi }{2}}^xK[1] \sin (K[1])dK[1]+1 \]

✓ Sympy. Time used: 0.127 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = - x \cos {\left (x \right )} + \sin {\left (x \right )} \]