78.3.12 problem 3 (b)

Internal problem ID [18115]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 3 (b)
Date solved : Tuesday, January 28, 2025 at 11:28:44 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve(diff(y(x),x)=sin(x-y(x)+1)^2,y(x), singsol=all)
 

\[ y = x +1+\arctan \left (-x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.313 (sec). Leaf size: 33

DSolve[D[y[x],x]==Sin[x-y[x]+1]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[2 y(x)-2 (\tan (-y(x)+x+1)-\arctan (\tan (-y(x)+x+1)))=c_1,y(x)] \]