Internal problem ID [10080]
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 1.3.4-2. Equations of
the form \((g_1(x)+g_0(x))y'=f_2(x) y^2+f_1(x) y+f_0(x)\)
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y x y^{\prime }-a y^{2}-b y-c \,x^{n}-s=0} \end {gather*}
✗ Solution by Maple
dsolve(x*y(x)*diff(y(x),x)=a*y(x)^2+b*y(x)+c*x^n+s,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y[x]*y'[x]==a*y[x]^2+b*y[x]+c*x^n+s,y[x],x,IncludeSingularSolutions -> True]
Not solved