24.50 problem 50

Internal problem ID [10044]

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: 50.
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 (x +4\right ) y}{5 x^{\frac {8}{5}}}-\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{\frac {3}{5}}}=0} \end {gather*}

Solution by Maple

dsolve(y(x)*diff(y(x),x)-1/5*a*(x+4)*x^(-8/5)*y(x)=1/5*a^2*(x-1)*(3*x+7)*x^(-3/5),y(x), singsol=all)
 

\[ \text {No solution found} \]

Solution by Mathematica

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

DSolve[y[x]*y'[x]-1/5*a*(x+4)*x^(-8/5)*y[x]==1/5*a^2*(x-1)*(3*x+7)*x^(-3/5),y[x],x,IncludeSingularSolutions -> True]
 

Not solved