Internal problem ID [9709]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.4-1. Equations with hyperbolic sine
and cosine
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\lambda \sinh \left (\lambda x \right ) y^{2}+\lambda \left (\sinh ^{3}\left (\lambda x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve(diff(y(x),x)=lambda*sinh(lambda*x)*y(x)^2-lambda*sinh(lambda*x)^3,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 c_{1} {\mathrm e}^{\cosh ^{2}\left (\lambda x \right )}}{\sqrt {\pi }\, \left (\erfi \left (\cosh \left (\lambda x \right )\right ) c_{1}+1\right )}+\frac {\cosh \left (\lambda x \right ) \erfi \left (\cosh \left (\lambda x \right )\right ) \sqrt {\pi }\, c_{1}+\cosh \left (\lambda x \right ) \sqrt {\pi }}{\sqrt {\pi }\, \left (\erfi \left (\cosh \left (\lambda x \right )\right ) c_{1}+1\right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Sinh[\[Lambda]*x]*y[x]^2-\[Lambda]*Sinh[\[Lambda]*x]^3,y[x],x,IncludeSingularSolutions -> True]
Not solved