24.4 problem 4

Internal problem ID [10741]

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: 4.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }-\left (\left (3-m \right ) x -1\right ) y=-\left (m -1\right ) a x} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=((3-m)*x-1)*y(x)+(m-1)*(x^2-x^2-a*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]==((3-m)*x-1)*y[x]+(m-1)*(x^2-x^2-a*x),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved