58.2.29 problem 29

Internal problem ID [9152]
Book : Second order enumerated odes
Section : section 2
Problem number : 29
Date solved : Monday, January 27, 2025 at 05:49:54 PM
CAS classification : [_Lienard]

\begin{align*} \cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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)
 

\[ y = \sec \left (x \right ) \left (c_{1} \sin \left (\sqrt {2}\, x \right )+c_{2} \cos \left (\sqrt {2}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 51

DSolve[Cos[x]^2*D[y[x],{x,2}]-2*Cos[x]*Sin[x]*D[y[x],x]+y[x]*Cos[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \sec (x) \]