Internal problem ID [9931]
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: 25.
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 {12 x}{49}-\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 1093
dsolve(y(x)*diff(y(x),x)-y(x)=-12/49*x+1/98*A*(25*x^(1/2)+41*A+10*A^2*x^(-1/2)),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-12/49*x+1/98*A*(25*x^(1/2)+41*A+10*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
Not solved