24.42 problem 42

Internal problem ID [10036]

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: 42.
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 (3 x -4\right ) y}{4 x^{\frac {5}{2}}}-\frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}}=0} \end {gather*}

Solution by Maple

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

\[ \text {No solution found} \]

Solution by Mathematica

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

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

Not solved