2.33 problem 33

Internal problem ID [10363]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power Functions
Problem number: 33.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-a \,x^{n} y^{2}-b \,x^{m} y=c k \,x^{k -1}-b c \,x^{k +m}-a \,c^{2} x^{n +2 k}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=a*x^n*y(x)^2+b*x^m*y(x)+c*k*x^(k-1)-b*c*x^(m+k)-a*c^2*x^(n+2*k),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*y[x]^2+b*x^m*y[x]+c*k*x^(k-1)-b*c*x^(m+k)-a*c^2*x^(n+2*k),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved