24.25 problem 25

Internal problem ID [10762]

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: 25.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}=a^{2} \left (-x^{2}+1\right )} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+1/2*a*(5*x+1)*x^(-1/2)*y(x)=a^2*(1-x^2),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*(5*x+1)*x^(-1/2)*y[x]==a^2*(1-x^2),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved