Internal problem ID [3871]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve((1+y(x)^2/x^2)-2*y(x)/x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x +x^{2}} \\ y \relax (x ) = -\sqrt {c_{1} x +x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 38
DSolve[(1+y[x]^2/x^2)-2*y[x]/x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ \end{align*}