61.7.8 problem 8

Internal problem ID [12159]
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 : 8
Date solved : Tuesday, January 28, 2025 at 12:45:48 AM
CAS classification : [_Riccati]

\begin{align*} x^{2} y^{\prime }&=x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4} \end{align*}

✗ Solution by Maple

dsolve(x^2*diff(y(x),x)=x^2*y(x)^2+a*(b*ln(x)+c)^n+1/4,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x^2*D[y[x],x]==x^2*y[x]^2+a*(b*Log[x]+c)^n+1/4,y[x],x,IncludeSingularSolutions -> True]
 

Not solved