Internal problem ID [9814]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\lambda \sin \left (\lambda x \right ) y^{2}-a \sin \left (\lambda x \right ) y+a \tan \left (\lambda x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
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)
\[ y \relax (x ) = \frac {\expIntegral \left (1, \frac {a \cos \left (\lambda x \right )}{\lambda }\right ) c_{1} a +1}{\cos \left (\lambda x \right ) \expIntegral \left (1, \frac {a \cos \left (\lambda x \right )}{\lambda }\right ) c_{1} a -{\mathrm e}^{-\frac {a \cos \left (\lambda x \right )}{\lambda }} c_{1} \lambda +\cos \left (\lambda x \right )} \]
✗ 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