Internal problem ID [2042]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {y \sin \left (x \right )-2 \cos \left (y\right )-\left (\cos \left (x \right )-2 \sin \left (y\right ) x +\sin \left (y\right )\right ) y^{\prime }=-\tan \left (x \right )} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve((y(x)*sin(x)-2*cos(y(x))+tan(x) )-(cos(x)-2*x*sin(y(x))+sin(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
\[ -y \cos \left (x \right )-2 x \cos \left (y\right )-\ln \left (\cos \left (x \right )\right )+\cos \left (y\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.673 (sec). Leaf size: 29
DSolve[(y[x]*Sin[x]-2*Cos[y[x]]+Tan[x] )-(Cos[x]-2*x*Sin[y[x]]+Sin[y[x]] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[4 x \cos (y(x))-2 \cos (y(x))+2 y(x) \cos (x)+2 \log (\cos (x))=c_1,y(x)] \]