Internal problem ID [10812]
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: 65.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime } y+\frac {a \left (\frac {\left (5+3 n \right ) x}{2}+\frac {-1+n}{n +1}\right ) x^{-\frac {4+n}{n +3}} y}{n +3}=-\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {5+n}{n +3}}}{2 n +6}} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)+a/(n+3)*((3*n+5)/(2)*x+(n-1)/(n+1))*x^(-(n+4)/(n+3))*y(x)=-a^2/(2*(n+3))*((n+1)*x^2-(n^2+2*n+5)/(n+1)*x+4/(n+1))*x^(-(n+5)/(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]+a/(n+3)*((3*n+5)/(2)*x+(n-1)/(n+1))*x^(-(n+4)/(n+3))*y[x]==-a^2/(2*(n+3))*((n+1)*x^2-(n^2+2*n+5)/(n+1)*x+4/(n+1))*x^(-(n+5)/(n+3)),y[x],x,IncludeSingularSolutions -> True]
Timed out