13.13 problem 59

Internal problem ID [10557]

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: 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)
 

\[ y \left (x \right ) = \frac {\operatorname {expIntegral}_{1}\left (\frac {a \cos \left (x \lambda \right )}{\lambda }\right ) c_{1} a +1}{\cos \left (x \lambda \right ) \operatorname {expIntegral}_{1}\left (\frac {a \cos \left (x \lambda \right )}{\lambda }\right ) c_{1} a -{\mathrm e}^{-\frac {a \cos \left (x \lambda \right )}{\lambda }} c_{1} \lambda +\cos \left (x \lambda \right )} \]

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