Internal problem ID [3918]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 21.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {y-y^{\prime } x}{y^{2}+y^{\prime }}-\frac {y-y^{\prime } x}{1+y^{\prime } x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 19
dsolve((y(x)-x*diff(y(x),x))/(y(x)^2+diff(y(x),x))=(y(x)-x*diff(y(x),x))/(1+x^2*diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x \\ y \relax (x ) = -\tanh \left (-\arctanh \relax (x )+c_{1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.124 (sec). Leaf size: 37
DSolve[(y[x]-x*y'[x])/(y[x]^2+y'[x])==(y[x]-x*y'[x])/(1+x^2*y'[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \cosh (c_1)-\sinh (c_1)}{\cosh (c_1)-x \sinh (c_1)} \\ y(x)\to c_1 x \\ \end{align*}