Internal problem ID [10627]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=-f \left (x \right )^{2}+f^{\prime }\left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x)=y(x)^2-f(x)^2+diff(f(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-f \left (x \right ) \left (\int {\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}d x \right )+f \left (x \right ) c_{1} +{\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}}{c_{1} -\left (\int {\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}d x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==y[x]^2-f[x]^2+f'[x],y[x],x,IncludeSingularSolutions -> True]
Not solved