Internal problem ID [4009]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.24, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (x -\cos \relax (y)\right ) y^{\prime }+\tan \relax (y)=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = \frac {\pi }{6}\right ] \end {align*}
✓ Solution by Maple
Time used: 17.408 (sec). Leaf size: 29
dsolve([(x-cos(y(x)))*diff(y(x),x)+tan(y(x))=0,y(1) = 1/6*Pi],y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-24 x \sin \left (\textit {\_Z} \right )+6 \sin \left (2 \textit {\_Z} \right )-2 \pi -3 \sqrt {3}+12 \textit {\_Z} +12\right ) \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 45
DSolve[{(x-Cos[y[x]])*y'[x]+Tan[y[x]]==0,{y[1]==Pi/6}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {1}{24} \left (12-3 \sqrt {3}-2 \pi \right ) \csc (y(x))+\left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right ) \csc (y(x)),y(x)\right ] \]