Internal problem ID [5364]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 1(n).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y \cos \relax (y)-\sin \relax (y)+x \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 15
dsolve((y(x)*cos(y(x))-sin(y(x))+x)*diff(y(x),x)=y(x),y(x), singsol=all)
\[ x -c_{1} y \relax (x )-\sin \left (y \relax (x )\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.234 (sec). Leaf size: 14
DSolve[(y[x]*Cos[y[x]]-Sin[y[x]]+x)*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x=\sin (y(x))+c_1 y(x),y(x)] \]