Internal problem ID [10047]
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: 53.
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 -6\right ) y}{5 x^{\frac {7}{5}}}-\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{\frac {9}{5}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 157
dsolve(y(x)*diff(y(x),x)+1/5*a*(x-6)*x^(-7/5)*y(x)=2/5*a^2*(x-1)*(x+4)*x^(-9/5),y(x), singsol=all)
\[ c_{1}+\frac {\sqrt {5}\, \sqrt {\frac {-y \relax (x ) x^{\frac {2}{5}}-\left (x -1\right ) a}{y \relax (x ) x^{\frac {2}{5}}+a x}}\, \left (-12 a y \relax (x ) x^{\frac {2}{5}}-\frac {3 x^{\frac {4}{5}} y \relax (x )^{2}}{2}+\left (-\frac {y \relax (x ) x^{\frac {7}{5}}}{2}+a \left (x +24\right ) \left (x -1\right )\right ) a \right ) \left (8 a y \relax (x ) x^{\frac {2}{5}}+x^{\frac {4}{5}} y \relax (x )^{2}+a \left (2 y \relax (x ) x^{\frac {7}{5}}+a \left (x +4\right )^{2}\right )\right ) \sqrt {15}}{54 \left (\frac {a}{y \relax (x ) x^{\frac {2}{5}}+a x}\right )^{\frac {5}{2}} \left (y \relax (x ) x^{\frac {2}{5}}+a x \right )^{2} \left (\left (x +4\right ) a +y \relax (x ) x^{\frac {2}{5}}\right )^{2} x} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+1/5*a*(x-6)*x^(-7/5)*y[x]==2/5*a^2*(x-1)*(x+4)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
Timed out