Internal problem ID [9774]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-2. Equations with cosine.
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\lambda \cos \left (\lambda x \right ) y^{2}-\lambda \left (\cos ^{3}\left (\lambda x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x)=lambda*cos(lambda*x)*y(x)^2+lambda*cos(lambda*x)^3,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\lambda x \right )+\frac {-1+2 c_{1}}{\left (\KummerU \left (1, \frac {3}{2}, -\left (\sin ^{2}\left (\lambda x \right )\right )\right ) c_{1}+\KummerM \left (1, \frac {3}{2}, -\left (\sin ^{2}\left (\lambda x \right )\right )\right )\right ) \sin \left (\lambda x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Cos[\[Lambda]*x]*y[x]^2+\[Lambda]*Cos[\[Lambda]*x]^3,y[x],x,IncludeSingularSolutions -> True]
Not solved