64.4.11 problem 11

Internal problem ID [13300]
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
Date solved : Tuesday, January 28, 2025 at 05:16:48 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x \tan \left (\frac {y}{x}\right )+y-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve((x*tan(y(x)/x)+y(x))- x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 9.511 (sec). Leaf size: 19

DSolve[(x*Tan[y[x]/x]+y[x])- x*D[y[x],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*}