Internal problem ID [9959]
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: 53.
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+\frac {12 x}{49}-A \sqrt {x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 127
dsolve(y(x)*diff(y(x),x)-y(x)=-12/49*x+A*x^(1/2),y(x), singsol=all)
\[ c_{1}+\frac {-7 \,14^{\frac {1}{3}} A \sqrt {3}+\frac {\sqrt {3}\, \left (4 x -7 y \relax (x )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {7}{6}\right ], \left [\frac {3}{2}\right ], \frac {3 \left (4 x -7 y \relax (x )\right )^{2}}{196 x^{\frac {3}{2}} A}\right ) \left (\frac {196 A \,x^{\frac {3}{2}}-48 x^{2}+168 x y \relax (x )-147 y \relax (x )^{2}}{A \,x^{\frac {3}{2}}}\right )^{\frac {1}{6}}}{7 \sqrt {x}}}{\left (\frac {196 A \,x^{\frac {3}{2}}-48 x^{2}+168 x y \relax (x )-147 y \relax (x )^{2}}{A \,x^{\frac {3}{2}}}\right )^{\frac {1}{6}} \sqrt {A \sqrt {x}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-12/49*x+A*x^(1/2),y[x],x,IncludeSingularSolutions -> True]
Not solved