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*}