61.2.45 problem 45

Internal problem ID [12051]
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 : 45
Date solved : Monday, January 27, 2025 at 11:54:31 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 827

dsolve((a__2*x+b__2)*(diff(y(x),x)+lambda*y(x)^2)+(a__1*x+b__1)*y(x)+a__0*x+b__0=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.230 (sec). Leaf size: 1432

DSolve[(a2*x+b2)*(D[y[x],x]+\[Lambda]*y[x]^2)+(a1*x+b1)*y[x]+a0*x+b0==0,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display