Internal problem ID [7932]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 352.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type unknown
Solve \begin {gather*} \boxed {y^{\prime } \left (\cos \relax (y)-\sin \left (\alpha \right ) \sin \relax (x )\right ) \cos \relax (y)+\left (\cos \relax (x )-\sin \left (\alpha \right ) \sin \relax (y)\right ) \cos \relax (x )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-sin(alpha)*sin(y(x)))*cos(x) = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.417 (sec). Leaf size: 43
DSolve[Cos[x]*(Cos[x] - Sin[\[Alpha]]*Sin[y[x]]) + Cos[y[x]]*(Cos[y[x]] - Sin[\[Alpha]]*Sin[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [4 \sin (\alpha ) \sin (x) \sin (y(x))-4 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 x-\sin (2 x)=c_1,y(x)\right ] \]