Internal problem ID [10517]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\cos \left (\lambda x \right ) y^{2} \lambda =\lambda \cos \left (\lambda x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {4 \csc \left (x \lambda \right ) \left (-\frac {\sqrt {\pi }\, \sin \left (x \lambda \right )^{2} \left (c_{1} -\frac {1}{2}\right ) \operatorname {erf}\left (\sqrt {-\sin \left (x \lambda \right )^{2}}\right )}{2}+\left (c_{1} -\frac {1}{2}\right ) {\mathrm e}^{\sin \left (x \lambda \right )^{2}} \sqrt {-\sin \left (x \lambda \right )^{2}}+\frac {\sin \left (x \lambda \right )^{2} \sqrt {\pi }\, c_{1}}{2}\right )}{\sqrt {\pi }\, \left (\operatorname {erf}\left (\sqrt {-\sin \left (x \lambda \right )^{2}}\right ) \left (2 c_{1} -1\right )-2 c_{1} \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==\[Lambda]*Cos[\[Lambda]*x]*y[x]^2+\[Lambda]*Cos[\[Lambda]*x]^3,y[x],x,IncludeSingularSolutions -> True]
Not solved