Internal problem ID [9603]
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: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-x^{2} y^{2}-a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}+\frac {n^{2}}{4}-\frac {1}{4}=0} \end {gather*}
✗ Solution by Maple
dsolve(x^2*diff(y(x),x)=x^2*y(x)^2+a*x^(2*m)*(b*x^m+c)^n+1/4*(1-n^2),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*y'[x]==x^2*y[x]^2+a*x^(2*m)*(b*x^m+c)^n+1/4*(1-n^2),y[x],x,IncludeSingularSolutions -> True]
Not solved