Internal problem ID [10042]
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: 48.
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 {2 a \left (3 x +2\right ) y}{5 x^{\frac {8}{5}}}-\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{\frac {11}{5}}}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-2/5*a*(3*x+2)*x^(-8/5)*y(x)=1/5*a^2*(x-1)*(8*x+1)*x^(-11/5),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-2/5*a*(3*x+2)*x^(-8/5)*y[x]==1/5*a^2*(x-1)*(8*x+1)*x^(-11/5),y[x],x,IncludeSingularSolutions -> True]
Timed out