Internal problem ID [10045]
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: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y y^{\prime }-\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 {11}{5}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 194
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^(-11/5),y(x), singsol=all)
\[ c_{1}-\frac {\left (\int _{}^{-\frac {315 \left (4 x^{\frac {3}{5}} y \relax (x )+4 x a -21 a \right )}{884 \left (x^{\frac {3}{5}} y \relax (x )+x a \right )}}\frac {\textit {\_a} \sqrt {52 \textit {\_a} -315}\, \left (68 \textit {\_a} +315\right )^{\frac {7}{6}}}{\left (221 \textit {\_a} +315\right )^{\frac {5}{3}} \left (-\frac {781456}{31255875} \textit {\_a}^{3}+\frac {79}{105} \textit {\_a} +1\right )}d \textit {\_a} \right ) x \left (\frac {a}{x^{\frac {3}{5}} y \relax (x )+x a}\right )^{\frac {5}{3}}-\frac {8 \,3^{\frac {1}{3}} \left (x -\frac {21}{4}\right ) \sqrt {255}\, 105^{\frac {1}{6}} \sqrt {\frac {-x^{\frac {3}{5}} y \relax (x )-\left (x -1\right ) a}{x^{\frac {3}{5}} y \relax (x )+x a}}\, 2^{\frac {1}{3}} 13^{\frac {5}{6}} \left (\frac {\left (3 x +7\right ) a +3 x^{\frac {3}{5}} y \relax (x )}{x^{\frac {3}{5}} y \relax (x )+x a}\right )^{\frac {7}{6}} 6615^{\frac {1}{3}}}{4444531}}{\left (\frac {a}{x^{\frac {3}{5}} y \relax (x )+x a}\right )^{\frac {5}{3}} x} = 0 \]
✗ 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^(-11/5),y[x],x,IncludeSingularSolutions -> True]
Timed out