Internal problem ID [7470]
Book: Second order enumerated odes
Section: section 2
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime } \sin \left (x \right )+\cos \left (x \right )^{2} y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
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)
\[ y \left (x \right ) = c_{1} \sec \left (x \right ) \sin \left (\sqrt {2}\, x \right )+c_{2} \sec \left (x \right ) \cos \left (\sqrt {2}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.098 (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]
\[ y(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \sec (x) \]