Internal problem ID [15151]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 289.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\cos \left (\frac {y}{2}+\frac {x}{2}\right )-\cos \left (-\frac {y}{2}+\frac {x}{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 62
dsolve(diff(y(x),x)+cos((x+y(x))/2)=cos((x-y(x))/2),y(x), singsol=all)
\[ y = 2 \arctan \left (\frac {2 \,{\mathrm e}^{-2 \cos \left (\frac {x}{2}\right )} c_{1}}{{\mathrm e}^{-4 \cos \left (\frac {x}{2}\right )} c_{1}^{2}+1}, \frac {-{\mathrm e}^{-4 \cos \left (\frac {x}{2}\right )} c_{1}^{2}+1}{{\mathrm e}^{-4 \cos \left (\frac {x}{2}\right )} c_{1}^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 70
DSolve[y'[x]+Cos[(x+y[x])/2]==Cos[(x-y[x])/2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \arccos \left (\tanh \left (\frac {1}{2} \left (4 \cos \left (\frac {x}{2}\right )-c_1\right )\right )\right ) \\ y(x)\to 2 \arccos \left (\tanh \left (\frac {1}{2} \left (4 \cos \left (\frac {x}{2}\right )-c_1\right )\right )\right ) \\ y(x)\to 0 \\ y(x)\to -2 \pi \\ y(x)\to 2 \pi \\ \end{align*}