25.5 problem 5

Internal problem ID [10822]

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: 5.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]

\[ \boxed {\left (y+a \,x^{1+n}+b \,x^{n}\right ) y^{\prime }-\left (x^{n} n a +c \,x^{n -1}\right ) y=0} \]

✗ Solution by Maple

dsolve((y(x)+a*x^(n+1)+b*x^n)*diff(y(x),x)=(a*n*x^n+c*x^(n-1))*y(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[(y[x]+a*x^(n+1)+b*x^n)*y'[x]==(a*n*x^n+c*x^(n-1))*y[x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved