35.4.12 problem 12

Internal problem ID [6130]
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
Date solved : Monday, January 27, 2025 at 01:37:50 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

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

\[ y = x \arcsin \left (\frac {1}{c_1 x}\right ) \]

✓ Solution by Mathematica

Time used: 11.984 (sec). Leaf size: 21

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

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