Internal problem ID [3892]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-a y+y^{2}-x^{-2 a}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 74
dsolve(x*diff(y(x),x)-a*y(x)+y(x)^2=x^(-2*a),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-x^{-a} c_{1}+a \right ) \sinh \left (\frac {x^{-a}}{a}\right )+\left (c_{1} a -x^{-a}\right ) \cosh \left (\frac {x^{-a}}{a}\right )}{\cosh \left (\frac {x^{-a}}{a}\right ) c_{1}+\sinh \left (\frac {x^{-a}}{a}\right )} \]
✓ Solution by Mathematica
Time used: 0.351 (sec). Leaf size: 73
DSolve[x*y'[x]-a*y[x]+y[x]^2==x^(-2*a),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a-\frac {x^{-a} \left (c_1 \coth \left (\frac {x^{-a}}{a}\right )+i\right )}{i \coth \left (\frac {x^{-a}}{a}\right )+c_1} \\ y(x)\to a-x^{-a} \coth \left (\frac {x^{-a}}{a}\right ) \\ \end{align*}