Internal problem ID [3880]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 4
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 53
dsolve(1/x+1/y(x)*diff(y(x),x)+2*(1/y(x)-1/x*diff(y(x),x))=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {c_{1} x}{2}-\frac {\sqrt {5 x^{2} c_{1}^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {\frac {c_{1} x}{2}+\frac {\sqrt {5 x^{2} c_{1}^{2}+4}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.465 (sec). Leaf size: 102
DSolve[1/x+1/y[x]*y'[x]+2*(1/y[x]-1/x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+x\right ) \\ \end{align*}