61.2.75 problem 75

Internal problem ID [12081]
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 : 75
Date solved : Tuesday, January 28, 2025 at 06:58:04 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 1236

dsolve((a*x^n+b*x^m+c)*diff(y(x),x)=c*y(x)^2-b*x^(m-1)*y(x)+a*x^(n-2),y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✗ Solution by Mathematica

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

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

Not solved