Internal problem ID [10567]
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: 59.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\lambda \sin \left (\lambda x \right ) y^{2}-a \sin \left (\lambda x \right ) y=-a \tan \left (\lambda x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(diff(y(x),x)=lambda*sin(lambda*x)*y(x)^2+a*sin(lambda*x)*y(x)-a*tan(lambda*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {Ei}_{1}\left (\frac {\cos \left (\lambda x \right ) a}{\lambda }\right ) c_{1} a -1}{\operatorname {Ei}_{1}\left (\frac {\cos \left (\lambda x \right ) a}{\lambda }\right ) \cos \left (\lambda x \right ) c_{1} a -{\mathrm e}^{-\frac {\cos \left (\lambda x \right ) a}{\lambda }} c_{1} \lambda -\cos \left (\lambda x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Sin[\[Lambda]*x]*y[x]^2+a*Sin[\[Lambda]*x]*y[x]-a*Tan[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
Not solved