6.1.7 problem 3(b)

Internal problem ID [1525]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 3(b)
Date solved : Tuesday, September 30, 2025 at 04:35:20 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x) = -x*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\sin \left (x \right )+x \cos \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\sin (x)+x \cos (x)+c_1 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + x \cos {\left (x \right )} - \sin {\left (x \right )} \]