61.13.1 problem 47

Internal problem ID [12221]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-5. Equations containing combinations of trigonometric functions.
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 01:24:05 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+lambda^2+c*sin(lambda*x)^n*cos(lambda*x)^(-n-4),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]==y[x]^2+\[Lambda]^2+c*Sin[\[Lambda]*x]^n*Cos[\[Lambda]*x]^(-n-4),y[x],x,IncludeSingularSolutions -> True]
 

Not solved