26.5.15 problem Exercise 11.16, page 97

Internal problem ID [6988]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.16, page 97
Date solved : Tuesday, September 30, 2025 at 04:07:48 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.176 (sec). Leaf size: 14

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

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