Internal problem ID [10014]
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: 20.
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 {2 b}{x^{2}}\right ) y}{2}-\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-1/2*a*(1+2*b*x^(-2))*y(x)=1/16*a^2*(3*x+4*b/x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-1/2*a*(1+2*b*x^(-2))*y[x]==1/16*a^2*(3*x+4*b/x),y[x],x,IncludeSingularSolutions -> True]
Not solved