75.2.8 problem 28

Internal problem ID [16685]
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
Date solved : Tuesday, January 28, 2025 at 09:17:58 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

Solution by Maple

Time used: 0.121 (sec). Leaf size: 14

dsolve(diff(y(x),x)=cos(x-y(x)),y(x), singsol=all)
 
\[ y = x -2 \,\operatorname {arccot}\left (-x +c_{1} \right ) \]

Solution by Mathematica

Time used: 4.978 (sec). Leaf size: 55

DSolve[D[y[x],x]==Cos[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to -i \log \left (\frac {e^{i x} (2 x-c_1)}{2 x-4 i-c_1}\right ) \\ y(x)\to -i \log \left (e^{i x}\right ) \\ \end{align*}