Internal problem ID [9910]
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: 4.
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-2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 109
dsolve(y(x)*diff(y(x),x)-y(x)=2*A*(x^(1/2)+4*A+3*A^2*x^(-1/2)),y(x), singsol=all)
\[ c_{1}+\frac {4 \arctanh \left (\frac {\sqrt {-\frac {A^{2}}{y \relax (x )}}\, \left (3 A +\sqrt {x}\right )}{\sqrt {\frac {-3 A^{2}-4 A \sqrt {x}-x +y \relax (x )}{y \relax (x )}}\, A}\right ) \sqrt {-\frac {A^{2}}{y \relax (x )}}-\sqrt {\frac {-6 A^{2}-8 A \sqrt {x}-2 x +2 y \relax (x )}{y \relax (x )}}\, \sqrt {2}}{\sqrt {-\frac {A^{2}}{y \relax (x )}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==2*A*(x^(1/2)+4*A+3*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
Not solved