Internal problem ID [10054]
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: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y-n \,x^{2 n} \left (x -a \right )^{-2 n -3}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-((n+1)*x-a*n)*x^(n-1)*(x-a)^(-n-2)*y(x)=n*x^(2*n)*(x-a)^(-2*n-3),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-((n+1)*x-a*n)*x^(n-1)*(x-a)^(-n-2)*y[x]==n*x^(2*n)*(x-a)^(-2*n-3),y[x],x,IncludeSingularSolutions -> True]
Not solved