67.1.16 problem 2.3 (f)

Internal problem ID [16281]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (f)
Date solved : Thursday, October 02, 2025 at 10:45:19 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \int _1^x\cos (K[1]) K[1]dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 12

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

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