73.7.25 problem 25

Internal problem ID [15183]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 07:40:33 AM
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: 10

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

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

✓ Solution by Mathematica

Time used: 9.176 (sec). Leaf size: 19

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