Internal problem ID [13127]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {y}{x}-\tan \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(diff(y(x),x)=y(x)/x+tan(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (c_{1} x \right ) x \]
✓ Solution by Mathematica
Time used: 4.007 (sec). Leaf size: 19
DSolve[y'[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*}