Internal problem ID [1915]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.349 (sec). Leaf size: 223
dsolve((x/y(x)+y(x)/x)*diff(y(x),x)+1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}\right )}}{x \left (c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}\right ) c_{1}} \\ y \relax (x ) = \frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}\right )}}{x \left (c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}\right ) c_{1}} \\ y \relax (x ) = -\frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}\right )}}{x \left (c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}\right ) c_{1}} \\ y \relax (x ) = -\frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}\right )}}{x \left (c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}\right ) c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 121
DSolve[(x/y[x]+y[x]/x)*y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-x^2-\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-x^2+\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-x^2+\sqrt {x^4+e^{4 c_1}}} \\ \end{align*}