58.2.29 problem 29

Internal problem ID [9152]
Book : Second order enumerated odes
Section : section 2
Problem number : 29
Date solved : Wednesday, March 05, 2025 at 07:35:01 AM
CAS classification : [_Lienard]

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

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

ode:=cos(x)^2*diff(diff(y(x),x),x)-2*cos(x)*sin(x)*diff(y(x),x)+cos(x)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*cos(x)**2 - 2*sin(x)*cos(x)*Derivative(y(x), x) + cos(x)**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False