Internal problem ID [4001]
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]
Solve \begin {gather*} \boxed {x y^{\prime }+y-x \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)+y(x)=x*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-x \cos \relax (x )+\sin \relax (x )+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.038 (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*}