Internal problem ID [9618]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-a \,x^{n} y^{2}+a \,x^{n} \left (b \,x^{m}+c \right ) y-b \,x^{m -1} m=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)=a*x^n*y(x)^2-a*x^n*(b*x^m+c)*y(x)+b*m*x^(m-1),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-a*x^n*(b*x^m+c)*y[x]+b*m*x^(m-1),y[x],x,IncludeSingularSolutions -> True]
Not solved