Internal problem ID [5241]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve((x*sin(y(x)/x)-y(x)*cos(y(x)/x))+(x*cos(y(x)/x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \arcsin \left (\frac {1}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 12.962 (sec). Leaf size: 21
DSolve[(x*Sin[y[x]/x]-y[x]*Cos[y[x]/x])+(x*Cos[y[x]/x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \arcsin \left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}