Internal problem ID [14955]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 2. The method of isoclines. Exercises page 27
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\cos \left (-y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 14
dsolve(diff(y(x),x)=cos(x-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = x -2 \,\operatorname {arccot}\left (c_{1} -x \right ) \]
✓ Solution by Mathematica
Time used: 0.45 (sec). Leaf size: 40
DSolve[y'[x]==Cos[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+2 \cot ^{-1}\left (x-\frac {c_1}{2}\right ) \\ y(x)\to x+2 \cot ^{-1}\left (x-\frac {c_1}{2}\right ) \\ y(x)\to x \\ \end{align*}