72.3.12 problem 3 (b)

Internal problem ID [19401]
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 : Thursday, October 02, 2025 at 04:22:15 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.214 (sec). Leaf size: 33

ode=D[y[x],x]==Sin[x-y[x]+1]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.492 (sec). Leaf size: 61

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x - y(x) + 1)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x - 2 \operatorname {atan}{\left (\frac {\sqrt {C_{1}^{2} + 2 C_{1} x + x^{2} + 1} - 1}{C_{1} + x} \right )} + 1, \ y{\left (x \right )} = x + 2 \operatorname {atan}{\left (\frac {\sqrt {C_{1}^{2} + 2 C_{1} x + x^{2} + 1} + 1}{C_{1} + x} \right )} + 1\right ] \]