61.20.1 problem 34

Internal problem ID [12303]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-2. Equations containing arbitrary functions and their derivatives.
Problem number : 34
Date solved : Tuesday, January 28, 2025 at 02:34:31 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

dsolve(diff(y(x),x)=y(x)^2-f(x)^2+diff(f(x),x),y(x), singsol=all)
 

\[ y = \frac {-f \left (\int {\mathrm e}^{2 \left (\int fd x \right )}d x \right )+f c_{1} +{\mathrm e}^{2 \left (\int fd x \right )}}{c_{1} -\int {\mathrm e}^{2 \left (\int fd x \right )}d x} \]

✗ Solution by Mathematica

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

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

Not solved