Internal problem ID [10659]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}}} \]
✗ Solution by Maple
dsolve(diff(y(x),x)=y(x)^2+lambda^2+sin(lambda*x+b)^(-4)*f(sin(lambda*x+a)/sin(lambda*x+b)),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+b]^(-4)*f[Sin[\[Lambda]*x+a]/Sin[\[Lambda]*x+b]],y[x],x,IncludeSingularSolutions -> True]
Not solved