61.21.1 problem 1

Internal problem ID [12312]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.9. Some Transformations
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 02:34:52 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+a^2*f(a*x+b),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==y[x]^2+a^2*f[a*x+b],y[x],x,IncludeSingularSolutions -> True]
 

Not solved