26.1.7 problem 3.b

Internal problem ID [4247]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 3.b
Date solved : Monday, January 27, 2025 at 08:44:20 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: 0.036 (sec). Leaf size: 13

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

\[ y \left (x \right ) = x +1+\arctan \left (-x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.335 (sec). Leaf size: 33

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

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