Internal problem ID [10794]
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: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y=a^{2} \left (k -2\right ) \left (x -1\right )^{2} x^{1-2 k}} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-a*( (k-2)*x + 2*k - 3)*x^(-k)*y(x)=a^2*(k-2)*(x-1)^2*x^(1-2*k),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*( (k-2)*x + 2*k - 3)*x^(-k)*y[x]==a^2*(k-2)*(x-1)^2*x^(1-2*k),y[x],x,IncludeSingularSolutions -> True]
Not solved