8.4 problem 209

Internal problem ID [2957]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 8
Problem number: 209.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime } x +\tan \relax (y)=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 12

dsolve(x*diff(y(x),x)+tan(y(x)) = 0,y(x), singsol=all)
 

\[ y \relax (x ) = \arcsin \left (\frac {1}{x c_{1}}\right ) \]

Solution by Mathematica

Time used: 15.595 (sec). Leaf size: 19

DSolve[x y'[x]+Tan[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {ArcSin}\left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}