Internal problem ID [9757]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\lambda \sin \left (\lambda x \right ) y^{2}-\lambda \sin \left (\lambda x \right )^{3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 63
dsolve(diff(y(x),x)=lambda*sin(lambda*x)*y(x)^2+lambda*sin(lambda*x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 c_{1} {\mathrm e}^{\cos \left (\lambda x \right )^{2}}}{\sqrt {\pi }\, \left (\operatorname {erfi}\left (\cos \left (\lambda x \right )\right ) c_{1} +1\right )}-\frac {\left (\sqrt {\pi }\, \operatorname {erfi}\left (\cos \left (\lambda x \right )\right ) c_{1} +\sqrt {\pi }\right ) \cos \left (\lambda x \right )}{\sqrt {\pi }\, \left (\operatorname {erfi}\left (\cos \left (\lambda x \right )\right ) c_{1} +1\right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Sin[\[Lambda]*x]*y[x]^2+\[Lambda]*Sin[\[Lambda]*x]^3,y[x],x,IncludeSingularSolutions -> True]
Not solved