7.5.61 problem 61

Internal problem ID [165]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 61
Date solved : Friday, February 07, 2025 at 07:59:42 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 23

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

\[ y = x -2 \arctan \left (\frac {c_1 -x +2}{-x +c_1}\right ) \]

✓ Solution by Mathematica

Time used: 0.377 (sec). Leaf size: 64

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

\[ \text {Solve}\left [y(x)-\sec (x-y(x)) \left (2 \sqrt {\cos ^2(x-y(x))} \arcsin \left (\frac {\sqrt {1-\sin (x-y(x))}}{\sqrt {2}}\right )+\sin (x-y(x))+1\right )=c_1,y(x)\right ] \]