26.1.4 problem 1.d

Internal problem ID [4244]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.d
Date solved : Monday, January 27, 2025 at 08:44:10 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {\left (\pi +2 \arcsin \left (\ln \left (x \right )+c_{1} \right )\right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.401 (sec). Leaf size: 34

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

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