61.2.64 problem 64

Internal problem ID [12070]
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 : 64
Date solved : Tuesday, January 28, 2025 at 12:13:28 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 2160

dsolve((c__2*x^2+b__2*x+a__2)*(diff(y(x),x)+lambda*y(x)^2)+(b__1*x+a__1)*y(x)+a__0=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 9.259 (sec). Leaf size: 1986

DSolve[(c2*x^2+b2*x+a2)*(D[y[x],x]+\[Lambda]*y[x]^2)+(b1*x+a1)*y[x]+a0==0,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display