Internal problem ID [6714]
Book: Second order enumerated odes
Section: section 2
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {\left (\cos ^{2}\relax (x )\right ) y^{\prime \prime }-2 \cos \relax (x ) \sin \relax (x ) y^{\prime }+\left (\cos ^{2}\relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(cos(x)^2*diff(y(x),x$2)-2*cos(x)*sin(x)*diff(y(x),x)+y(x)*cos(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (x \sqrt {2}\right )}{\cos \relax (x )}+\frac {c_{2} \cos \left (x \sqrt {2}\right )}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 51
DSolve[Cos[x]^2*y''[x]-2*Cos[x]*Sin[x]*y'[x]+y[x]*Cos[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \sec (x) \\ \end{align*}