Internal problem ID [9598]
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: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x^{2 n} a +b \,x^{n -1}\right ) y^{2}-c=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 6615
dsolve(diff(y(x),x)=(a*x^(2*n)+b*x^(n-1))*y(x)^2+c,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==(a*x^(2*n)+b*x^(n-1))*y[x]^2+c,y[x],x,IncludeSingularSolutions -> True]
Not solved