61.2.71 problem 71

Internal problem ID [12077]
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 : 71
Date solved : Tuesday, January 28, 2025 at 12:14:24 AM
CAS classification : [_rational, _Riccati]

\begin{align*} a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s&=0 \end{align*}

✗ Solution by Maple

dsolve(a*(x^2-1)*(diff(y(x),x)+lambda*y(x)^2)+b*x*(x^2-1)*y(x)+c*x^2+d*x+s=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[a*(x^2-1)*(D[y[x],x]+\[Lambda]*y[x]^2)+b*x*(x^2-1)*y[x]+c*x^2+d*x+s==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved