18.1.26 problem Problem 14.30 (b)

Internal problem ID [3482]
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)
Date solved : Monday, January 27, 2025 at 07:38:49 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\pi }{2} \end{align*}

✓ Solution by Maple

Time used: 11.175 (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)
 

\[ y \left (x \right ) = \arcsin \left (\frac {x}{2}+\frac {\sqrt {x^{2}+4}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 18.142 (sec). Leaf size: 67

DSolve[{(2*Sin[y[x]]-x)*D[y[x],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*}