Internal problem ID [14986]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\sin \left (-y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 23
dsolve(diff(y(x),x)=sin(x-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = x -2 \arctan \left (\frac {2-x +c_{1}}{c_{1} -x}\right ) \]
✓ Solution by Mathematica
Time used: 0.415 (sec). Leaf size: 64
DSolve[y'[x]==Sin[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-\sec (x-y(x)) \left (2 \sqrt {\cos ^2(x-y(x))} \arcsin \left (\frac {\sqrt {1-\sin (x-y(x))}}{\sqrt {2}}\right )+\sin (x-y(x))+1\right )=c_1,y(x)\right ] \]