61.9.6 problem 6

Internal problem ID [12180]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-1. Equations with sine
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:51:52 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

dsolve(diff(y(x),x)=lambda*sin(lambda*x)*y(x)^2+lambda*sin(lambda*x)^3,y(x), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{\frac {\cos \left (2 \lambda x \right )}{2}+\frac {1}{2}} c_{1} -\cos \left (\lambda x \right ) \sqrt {\pi }\, \left (\operatorname {erfi}\left (\cos \left (\lambda x \right )\right ) c_{1} +1\right )}{\sqrt {\pi }\, \left (\operatorname {erfi}\left (\cos \left (\lambda x \right )\right ) c_{1} +1\right )} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==\[Lambda]*Sin[\[Lambda]*x]*y[x]^2+\[Lambda]*Sin[\[Lambda]*x]^3,y[x],x,IncludeSingularSolutions -> True]
 

Not solved