75.4.14 problem 59

Internal problem ID [16637]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 59
Date solved : Thursday, March 13, 2025 at 08:28:22 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.107 (sec). Leaf size: 23

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

\[ y = x -2 \arctan \left (\frac {-x +2+c_{1}}{-x +c_{1}}\right ) \]

✓ Mathematica. Time used: 0.341 (sec). Leaf size: 201

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

\[ \text {Solve}\left [\int _1^x-\exp \left (\int _1^{K[2]-y(x)}\left (1+\frac {2}{\cot \left (\frac {K[1]}{2}\right )-1}\right )dK[1]\right ) \sin (K[2]-y(x))dK[2]+\int _1^{y(x)}\left (\exp \left (\int _1^{x-K[3]}\left (1+\frac {2}{\cot \left (\frac {K[1]}{2}\right )-1}\right )dK[1]\right )-\int _1^x\left (\exp \left (\int _1^{K[2]-K[3]}\left (1+\frac {2}{\cot \left (\frac {K[1]}{2}\right )-1}\right )dK[1]\right ) \cos (K[2]-K[3])-\exp \left (\int _1^{K[2]-K[3]}\left (1+\frac {2}{\cot \left (\frac {K[1]}{2}\right )-1}\right )dK[1]\right ) \left (-1-\frac {2}{\cot \left (\frac {1}{2} (K[2]-K[3])\right )-1}\right ) \sin (K[2]-K[3])\right )dK[2]\right )dK[3]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.694 (sec). Leaf size: 15

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

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