61.24.71 problem 71

Internal problem ID [12484]
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 : 71
Date solved : Tuesday, January 28, 2025 at 03:16:56 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=exp(a*x)*(2*a*x^2+2*x+b)*y(x)+exp(2*a*x)*(-a*x^4-b*x^2+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]==Exp[a*x]*(2*a*x^2+2*x+b)*y[x]+Exp[2*a*x]*(-a*x^4-b*x^2+c),y[x],x,IncludeSingularSolutions -> True]
 

Not solved