Internal problem ID [10800]
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`]]
\[ \boxed {y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{\frac {7}{5}}}=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{\frac {9}{5}}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ c_{1} +\frac {\left (-12 a y \left (x \right ) x^{\frac {2}{5}}-\frac {3 x^{\frac {4}{5}} y \left (x \right )^{2}}{2}+\left (-\frac {y \left (x \right ) x^{\frac {7}{5}}}{2}+a \left (x +24\right ) \left (x -1\right )\right ) a \right ) \left (8 a y \left (x \right ) x^{\frac {2}{5}}+x^{\frac {4}{5}} y \left (x \right )^{2}+a \left (2 y \left (x \right ) x^{\frac {7}{5}}+a \left (x +4\right )^{2}\right )\right ) \sqrt {5}\, \sqrt {15}\, \sqrt {\frac {-\left (x -1\right ) a -y \left (x \right ) x^{\frac {2}{5}}}{y \left (x \right ) x^{\frac {2}{5}}+a x}}}{54 \left (\frac {a}{y \left (x \right ) x^{\frac {2}{5}}+a x}\right )^{\frac {5}{2}} \left (a \left (x +4\right )+y \left (x \right ) x^{\frac {2}{5}}\right )^{2} x \left (y \left (x \right ) x^{\frac {2}{5}}+a x \right )^{2}} = 0 \]
✗ 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