Internal problem ID [10032]
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: 38.
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 (39 x -4\right ) y}{42 x^{\frac {9}{7}}}+\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{\frac {11}{7}}}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)+1/42*a*(39*x-4)*x^(-9/7)*y(x)=-1/42*a^2*(x-1)*(9*x-1)*x^(-11/7),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+1/42*a*(39*x-4)*x^(-9/7)*y[x]==-1/42*a^2*(x-1)*(9*x-1)*x^(-11/7),y[x],x,IncludeSingularSolutions -> True]
Timed out