61.24.13 problem 13

Internal problem ID [12426]
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 : 13
Date solved : Tuesday, January 28, 2025 at 03:01:30 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y&=\left (a \left (2 n +1\right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=(a*(2*n+1)*x^2+c*x+b*(2*n-1))*x^(n-2)*y(x)-(n*a^2*x^4+a*c*x^3+d*x^2+b*c*x+n*b^2)*x^(2*n-3),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+1)*x^2+c*x+b*(2*n-1))*x^(n-2)*y[x]-(n*a^2*x^4+a*c*x^3+d*x^2+b*c*x+n*b^2)*x^(2*n-3),y[x],x,IncludeSingularSolutions -> True]
 

Timed out