Internal problem ID [2587]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
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: 0.031 (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: 0.034 (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*}