Internal problem ID [9992]
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. subsection 1.3.2. Equations of the
form \(y y'=f(x) y+1\)
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-a y \sinh \relax (x )-1=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=a*y(x)*sinh(x)+1,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]==a*y[x]*Sinh[x]+1,y[x],x,IncludeSingularSolutions -> True]
Not solved