61.24.11 problem 11

Internal problem ID [12424]
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.
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 03:00:13 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y&=\left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=(a*(2*n+k)*x^(2*k)+b*(2*m-k))*x^(m-k-1)*y(x)-(a^2*m*x^(4*k)+c*x^(2*k)+b^2*m)*x^(2*m-2*m-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]==(a*(2*n+k)*x^(2*k)+b*(2*m-k))*x^(m-k-1)*y[x]-(a^2*m*x^(4*k)+c*x^(2*k)+b^2*m)*x^(2*m-2*m-1),y[x],x,IncludeSingularSolutions -> True]
 

Timed out