61.22.6 problem 6

Internal problem ID [12331]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 02:47:12 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1} \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],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