Internal problem ID [9904]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}-\lambda ^{2}-\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)=y(x)^2+lambda^2+sin(lambda*x)^(-4)*f(cot(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+Sin[\[Lambda]*x]^(-4)*f[Cot[\[Lambda]*x]],y[x],x,IncludeSingularSolutions -> True]
Not solved