Internal problem ID [9912]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 6.
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-y-A \,x^{k -1}+k B \,x^{k}-k \,B^{2} x^{2 k -1}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=A*x^(k-1)-k*B*x^k+k*B^2*x^(2*k-1),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==A*x^(k-1)-k*B*x^k+k*B^2*x^(2*k-1),y[x],x,IncludeSingularSolutions -> True]
Not solved