50.1.13 problem 1(n)

Internal problem ID [7785]
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)
Date solved : Monday, January 27, 2025 at 03:23:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

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

\[ x -c_{1} y-\sin \left (y\right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.229 (sec). Leaf size: 14

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

\[ \text {Solve}[x=\sin (y(x))+c_1 y(x),y(x)] \]