25.1.18 problem 18

Internal problem ID [4230]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 18
Date solved : Monday, January 27, 2025 at 08:43:09 AM
CAS classification : [_separable]

\begin{align*} x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.244 (sec). Leaf size: 8

dsolve([x*cos(y(x))*diff(y(x),x)=1+sin(y(x)),y(1) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 52.772 (sec). Leaf size: 53

DSolve[{x*Cos[y[x]]*D[y[x],x]==1+Sin[y[x]],y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -2 \arccos \left (\frac {1}{2} \left (\sqrt {2-x}+\sqrt {x}\right )\right ) \\ y(x)\to 2 \arccos \left (\frac {1}{2} \left (\sqrt {2-x}+\sqrt {x}\right )\right ) \\ \end{align*}