Internal problem ID [10648]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}}} \]
✗ Solution by Maple
dsolve(diff(y(x),x)=y(x)^2+lambda^2+cos(lambda*x)^(-4)*f(tan(lambda*x)),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==y[x]^2+\[Lambda]^2+Cos[\[Lambda]*x]^(-4)*f[Tan[\[Lambda]*x]],y[x],x,IncludeSingularSolutions -> True]
Not solved