Internal problem ID [9738]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-1. Equations Containing
Logarithmic Functions
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -a \,x^{n} y^{2}-b +a \,b^{2} x^{n} \ln \relax (x )^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve(x*diff(y(x),x)=a*x^n*y(x)^2+b-a*b^2*x^n*(ln(x))^2,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y'[x]==a*x^n*y[x]^2+b-a*b^2*x^n*(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
Not solved