Internal problem ID [10452]
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]
\[ \boxed {y^{\prime }-\lambda \sinh \left (\lambda x \right ) y^{2}=-\lambda \sinh \left (\lambda x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(y(x),x)=lambda*sinh(lambda*x)*y(x)^2-lambda*sinh(lambda*x)^3,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \left ({\mathrm e}^{\frac {\cosh \left (2 x \lambda \right )}{2}+\frac {1}{2}} c_{1} -\frac {\cosh \left (x \lambda \right ) \sqrt {\pi }\, \left (\operatorname {erfi}\left (\cosh \left (x \lambda \right )\right ) c_{1} +1\right )}{2}\right )}{\sqrt {\pi }\, \left (\operatorname {erfi}\left (\cosh \left (x \lambda \right )\right ) c_{1} +1\right )} \]
✗ 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