Internal problem ID [9928]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 22.
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-y+\frac {4 x}{25}-\frac {A}{\sqrt {x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 165
dsolve(y(x)*diff(y(x),x)-y(x)=-4/25*x+A*x^(-1/2),y(x), singsol=all)
\[ c_{1}+\frac {\frac {4 \left (10 x A -4 \sqrt {A \,x^{\frac {3}{2}}}\, x +5 \sqrt {A \,x^{\frac {3}{2}}}\, y \relax (x )\right ) \left (10 x A +4 \sqrt {A \,x^{\frac {3}{2}}}\, x -5 \sqrt {A \,x^{\frac {3}{2}}}\, y \relax (x )\right ) \left (4 x -5 y \relax (x )\right ) \left (150 A \sqrt {x}-16 x^{2}+40 x y \relax (x )-25 y \relax (x )^{2}\right )}{A^{2} x^{\frac {3}{2}} \left (100 A \sqrt {x}-16 x^{2}+40 x y \relax (x )-25 y \relax (x )^{2}\right )}-5000 A}{\left (\frac {100 A \sqrt {x}-16 x^{2}+40 x y \relax (x )-25 y \relax (x )^{2}}{A \sqrt {x}}\right )^{\frac {3}{2}} \sqrt {A \,x^{\frac {3}{2}}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-4/25*x+A*x^(-1/2),y[x],x,IncludeSingularSolutions -> True]
Not solved