4.12 problem 12

Internal problem ID [4278]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number: 12.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}+\tan \left (\frac {y}{x}\right )=0} \end {gather*}

Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve(diff(y(x),x)=y(x)/x- tan(y(x)/x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 2.328 (sec). Leaf size: 21

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

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