Internal problem ID [4379]
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]
\[ \boxed {\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((1+y(x)^2/x^2)-2*y(x)/x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {\left (x +c_{1} \right ) x} \\ y \left (x \right ) &= -\sqrt {\left (x +c_{1} \right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (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*}