Internal problem ID [2002]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.30 (b).
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 (2 \sin \relax (y)-x \right ) y^{\prime }-\tan \relax (y)=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 4.37 (sec). Leaf size: 18
dsolve([(2*sin(y(x))-x)*diff(y(x),x)=tan(y(x)),y(0) = 1/2*Pi],y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {x}{2}+\frac {\sqrt {x^{2}+4}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 10.565 (sec). Leaf size: 67
DSolve[{(2*Sin[y[x]]-x)*y'[x]==Tan[y[x]],y[0]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot ^{-1}\left (\sqrt {\frac {x^2}{2}-\frac {1}{2} \sqrt {x^4+4 x^2}}\right ) \\ y(x)\to \cot ^{-1}\left (\frac {\sqrt {x^2+\sqrt {x^2 \left (x^2+4\right )}}}{\sqrt {2}}\right ) \\ \end{align*}