Internal problem ID [4000]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x +y-\sin \left (x \right ) x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)+y(x)=x*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-x \cos \left (x \right )+\sin \left (x \right )+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 19
DSolve[x*y'[x]+y[x]==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (x)-x \cos (x)+c_1}{x} \\ \end{align*}