Internal problem ID [9997]
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. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 y^{\prime } y-\left (7 x a +5 b \right ) y+3 a^{2} x^{3}+2 c \,x^{2}+3 b^{2} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 2909
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: 0.0 (sec). Leaf size: 0
DSolve[2*y[x]*y'[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