Internal problem ID [9943]
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: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-2 A^{2}+A \sqrt {x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 156
dsolve(y(x)*diff(y(x),x)-y(x)=2*A^2-A*x^(1/2),y(x), singsol=all)
\[ c_{1}+\frac {\left (-2 A +\sqrt {x}\right ) \BesselK \left (1, -\sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}\right )+\BesselK \left (0, -\sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}\, A}{\left (-2 A +\sqrt {x}\right ) \BesselI \left (1, \sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}\right )+A \BesselI \left (0, \sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y \relax (x )}{A^{2}}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==2*A^2-A*x^(1/2),y[x],x,IncludeSingularSolutions -> True]
Not solved