61.5.4 problem 4

Internal problem ID [12128]
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
Date solved : Tuesday, January 28, 2025 at 12:26:27 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.004 (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)
 

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

✗ Solution by Mathematica

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

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

Not solved