24.41 problem 41

Internal problem ID [10035]

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: 41.
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 (1-\frac {b}{x^{2}}\right ) y}{x}-\frac {a^{2} b}{x}=0} \end {gather*}

Solution by Maple

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

Not solved