61.23.12 problem 12

Internal problem ID [12413]
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.
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 02:59:04 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y&=a \sin \left (\lambda x \right ) y+1 \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=a*sin(lambda*x)*y(x)+1,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*Sin[\[Lambda]*x]*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

Not solved