Internal problem ID [10527]
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]
\[ \boxed {y^{\prime }-\cos \left (\lambda x \right ) y^{2} \lambda =\cos \left (\lambda x \right )^{3} \lambda } \]
✓ 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)
\[ y \left (x \right ) = \sin \left (\lambda x \right )+\frac {2 c_{1} -1}{\left (\operatorname {KummerU}\left (1, \frac {3}{2}, -\sin \left (\lambda x \right )^{2}\right ) c_{1} +\operatorname {KummerM}\left (1, \frac {3}{2}, -\sin \left (\lambda x \right )^{2}\right )\right ) \sin \left (\lambda x \right )} \]
✗ 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