Internal problem ID [4426]
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]
\[ \boxed {\frac {y-x y^{\prime }}{y^{2}+y^{\prime }}-\frac {y-x y^{\prime }}{1+x^{2} y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.032 (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 \left (x \right ) &= c_{1} x \\ y \left (x \right ) &= -\tanh \left (-\operatorname {arctanh}\left (x \right )+c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.122 (sec). Leaf size: 45
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+e^{2 c_1} (x-1)+1}{-x+e^{2 c_1} (x-1)-1} \\ y(x)\to c_1 x \\ \end{align*}