32.5.15 problem Exercise 11.16, page 97

Internal problem ID [5853]
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 : Monday, January 27, 2025 at 01:20:51 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 19

DSolve[x*D[y[x],x]+y[x]==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)-x \cos (x)+c_1}{x} \]