Internal problem ID [10027]
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: 33.
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 (4 x +3\right ) y}{14 x^{\frac {8}{7}}}+\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{\frac {9}{7}}}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-1/14*a*(4*x+3)*x^(-8/7)*y(x)=-1/14*a^2*(x-1)*(16*x+5)*x^(-9/7),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-1/14*a*(4*x+3)*x^(-8/7)*y[x]==-1/14*a^2*(x-1)*(16*x+5)*x^(-9/7),y[x],x,IncludeSingularSolutions -> True]
Timed out