Internal problem ID [10070]
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 1.3.3-2. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 76.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (\sinh \relax (x ) a +b \right ) y+a b \cosh \relax (x )-c=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=(a*sinh(x)+b)*y(x)-a*b*cosh(x)+c,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*Sinh[x]+b)*y[x]-a*b*Cosh[x]+c,y[x],x,IncludeSingularSolutions -> True]
Not solved