Internal problem ID [10056]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.3-2. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y-a^{2} \left (\left (k +n -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-a*((n+2*k-3)*x+3-2*k)*x^(-k)*y(x)=a^2*((n+k-1)*x^2-(n+2*k-3)*x+k-2)*x^(1-2*k),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-a*((n+2*k-3)*x+3-2*k)*x^(-k)*y[x]==a^2*((n+k-1)*x^2-(n+2*k-3)*x+k-2)*x^(1-2*k),y[x],x,IncludeSingularSolutions -> True]
Timed out