Internal problem ID [3069]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.188 (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: 37.067 (sec). Leaf size: 53
DSolve[{x*Cos[y[x]]*y'[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*}