61.24.3 problem 3

Internal problem ID [12416]
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 : 3
Date solved : Tuesday, January 28, 2025 at 07:58:22 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 y^{\prime } y&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 4589

dsolve(2*y(x)*diff(y(x),x)=(7*a*x+5*b)*y(x)-3*a^2*x^3-2*c*x^2-3*b^2*x,y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✗ Solution by Mathematica

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

DSolve[2*y[x]*D[y[x],x]==(7*a*x+5*b)*y[x]-3*a^2*x^3-2*c*x^2-3*b^2*x,y[x],x,IncludeSingularSolutions -> True]
 

Not solved