Internal problem ID [4388]
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`]]
\[ \boxed {\frac {2}{y}-\frac {2 y^{\prime }}{x}=-\frac {1}{x}-\frac {y^{\prime }}{y}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 51
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 \left (x \right ) &= \frac {c_{1} x -\sqrt {5 x^{2} c_{1}^{2}+4}}{2 c_{1}} \\ y \left (x \right ) &= \frac {c_{1} x +\sqrt {5 x^{2} c_{1}^{2}+4}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.46 (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*}