Internal problem ID [10055]
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: 61.
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 (-3+2 k \right ) x +1\right ) x^{-k} y-a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{-2 k +2}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-a*((2*k-3)*x+1)*x^(-k)*y(x)=a^2*(k-2)*((k-1)*x+1)*x^(2*(1-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*((2*k-3)*x+1)*x^(-k)*y[x]==a^2*(k-2)*((k-1)*x+1)*x^(2*(1-k)),y[x],x,IncludeSingularSolutions -> True]
Not solved