24.47 problem 47

Internal problem ID [10784]

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: 47.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]

\[ \boxed {y y^{\prime }+\frac {a \left (24 x +11\right ) x^{\frac {27}{20}} y}{30}=-\frac {a^{2} \left (x -1\right ) \left (9 x +1\right )}{60 x^{\frac {17}{10}}}} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+1/30*a*(24*x+11)*x^(27/20)*y(x)=-1/60*a^2*(x-1)*(9*x+1)*x^(-17/10),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y[x]*y'[x]+1/30*a*(24*x+11)*x^(27/20)*y[x]==-1/60*a^2*(x-1)*(9*x+1)*x^(-17/10),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Timed out