Internal problem ID [10606]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \tan \left (\frac {y}{x}\right )+y-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve((x*tan(y(x)/x)+y(x))- x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (x c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 5.033 (sec). Leaf size: 19
DSolve[(x*Tan[y[x]/x]+y[x])- x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}