Internal problem ID [9863]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary
functions (but not containing their derivatives).
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-{\mathrm e}^{\lambda x} f \left (x \right ) y^{2}-\left (a f \left (x \right )-\lambda \right ) y-b \,{\mathrm e}^{-\lambda x} f \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 68
dsolve(diff(y(x),x)=exp(lambda*x)*f(x)*y(x)^2+(a*f(x)-lambda)*y(x)+b*exp(-lambda*x)*f(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left ({\mathrm e}^{\lambda x} {\mathrm e}^{-\lambda x} a^{2}+\tanh \left (\frac {\sqrt {a^{4}-4 a^{2} b}\, \left (a \left (\int f \left (x \right )d x \right )+c_{1} \right )}{2 a^{2}}\right ) \sqrt {a^{4}-4 a^{2} b}\right ) {\mathrm e}^{-\lambda x}}{2 a} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==Exp[\[Lambda]*x]*f[x]*y[x]^2+(a*f[x]-\[Lambda])*y[x]+b*Exp[-\[Lambda]*x]*f[x],y[x],x,IncludeSingularSolutions -> True]
Timed out