83.4.11 problem 11

Internal problem ID [19083]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 12:53:08 PM
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: 11

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

\[ y \left (x \right ) = \arccos \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.402 (sec). Leaf size: 30

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*}