Internal problem ID [10622]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\lambda \sin \left (\lambda x \right ) y^{2}-f \left (x \right ) \cos \left (\lambda x \right ) y=-f \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\sec \left (x \lambda \right ) \lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x} \sin \left (x \lambda \right )d x \right ) c_{1} -c_{1} {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x}-\sec \left (x \lambda \right )}{\lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x} \sin \left (x \lambda \right )d x \right ) c_{1} -1} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Sin[\[Lambda]*x]*y[x]^2+f[x]*Cos[\[Lambda]*x]*y[x]-f[x],y[x],x,IncludeSingularSolutions -> True]
Not solved