Internal problem ID [10034]
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: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y+\frac {a \left (3 x -2\right ) y}{x}+\frac {2 a^{2} \left (x -1\right )^{2}}{x}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)+a*(3*x-2)*x^(-1)*y(x)=-2*a^2*(x-1)^2*x^(-1),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*(3*x-2)*x^(-1)*y[x]==-2*a^2*(x-1)^2*x^(-1),y[x],x,IncludeSingularSolutions -> True]
Not solved