61.19.29 problem 29

Internal problem ID [12298]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary functions (but not containing their derivatives).
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 02:20:20 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 97

dsolve(diff(y(x),x)=lambda*sin(lambda*x)*y(x)^2+f(x)*cos(lambda*x)*y(x)-f(x),y(x), singsol=all)
 

\[ y = \frac {-c_{1} {\mathrm e}^{\int \left (f \cos \left (\lambda x \right )+2 \tan \left (\lambda x \right ) \lambda \right )d x}+\sec \left (\lambda x \right ) \lambda \left (\int {\mathrm e}^{\int \left (f \cos \left (\lambda x \right )+2 \tan \left (\lambda x \right ) \lambda \right )d x} \sin \left (\lambda x \right )d x \right ) c_{1} -\sec \left (\lambda x \right )}{\lambda \left (\int {\mathrm e}^{\int \left (f \cos \left (\lambda x \right )+2 \tan \left (\lambda x \right ) \lambda \right )d x} \sin \left (\lambda x \right )d x \right ) c_{1} -1} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]==\[Lambda]*Sin[\[Lambda]*x]*y[x]^2+f[x]*Cos[\[Lambda]*x]*y[x]-f[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved