Internal problem ID [10800]
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: 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-\frac {a \left (\left (2+n \right ) x -2\right ) x^{-\frac {2 n +1}{n}} y}{n}=\frac {a^{2} \left (\left (1+n \right ) x^{2}-2 x -n +1\right ) x^{-\frac {2+3 n}{n}}}{n}} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-a/n*((n+2)*x-2)*x^(-(2*n+1)/n)*y(x)=a^2/n*((n+1)*x^2-2*x-n+1)*x^(-(3*n+2)/n),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*((n+2)*x-2)*x^(-(2*n+1)/n)*y[x]==a^2/n*((n+1)*x^2-2*x-n+1)*x^(-(3*n+2)/n),y[x],x,IncludeSingularSolutions -> True]
Not solved