2.29 problem 29

Internal problem ID [10359]

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: 29.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }+\left (n +1\right ) x^{n} y^{2}=a \,x^{1+m +n}-a \,x^{m}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=-(n+1)*x^n*y(x)^2+a*x^(n+m+1)-a*x^m,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y'[x]==-(n+1)*x^n*y[x]^2+a*x^(n+m+1)-a*x^m,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved