61.24.79 problem 79

Internal problem ID [12492]
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 : 79
Date solved : Tuesday, January 28, 2025 at 03:17:39 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y&=a x \cos \left (\lambda \,x^{2}\right ) y+x \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=a*x*cos(lambda*x^2)*y(x)+x,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*x*Cos[\[Lambda]*x^2]*y[x]+x,y[x],x,IncludeSingularSolutions -> True]
 

Not solved