61.10.6 problem 19

Internal problem ID [12193]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-2. Equations with cosine.
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 01:01:32 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 95

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

\[ y = -\frac {4 \csc \left (\lambda x \right ) \left (-\frac {\sqrt {\pi }\, \sin \left (\lambda x \right )^{2} \left (-\frac {1}{2}+c_{1} \right ) \operatorname {erf}\left (\sqrt {-\sin \left (\lambda x \right )^{2}}\right )}{2}+\left (-\frac {1}{2}+c_{1} \right ) {\mathrm e}^{\sin \left (\lambda x \right )^{2}} \sqrt {-\sin \left (\lambda x \right )^{2}}+\frac {\sqrt {\pi }\, \sin \left (\lambda x \right )^{2} c_{1}}{2}\right )}{\sqrt {\pi }\, \left (\operatorname {erf}\left (\sqrt {-\sin \left (\lambda x \right )^{2}}\right ) \left (2 c_{1} -1\right )-2 c_{1} \right )} \]

✗ Solution by Mathematica

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

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

Not solved