15.2.13 problem 13

Internal problem ID [2883]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 13
Date solved : Monday, January 27, 2025 at 06:24:30 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 44

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

\[ y = \arctan \left (\frac {2 x c_1}{c_1^{2} x^{2}+1}, \frac {-c_1^{2} x^{2}+1}{c_1^{2} x^{2}+1}\right ) x \]

✓ Solution by Mathematica

Time used: 0.322 (sec). Leaf size: 52

DSolve[D[y[x],x]*x-y[x]-x*Sin[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \arccos (-\tanh (\log (x)+c_1)) \\ y(x)\to x \arccos (-\tanh (\log (x)+c_1)) \\ y(x)\to 0 \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}