61.24.75 problem 75

Internal problem ID [12488]
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.
Problem number : 75
Date solved : Tuesday, January 28, 2025 at 03:17:16 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y&=\left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=(a*cosh(x)+b)*y(x)-a*b*sinh(x)+c,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]==(a*Cosh[x]+b)*y[x]-a*b*Sinh[x]+c,y[x],x,IncludeSingularSolutions -> True]
 

Not solved