Internal problem ID [5436]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 13
dsolve(-1/y(x)*sin(x/y(x))+(x/y(x)^2*sin(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\pi -c_{1}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 19
DSolve[-1/y[x]*Sin[x/y[x]]+(x/y[x]^2*Sin[x/y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to \text {ComplexInfinity} \\ y(x)\to \text {ComplexInfinity} \\ \end{align*}