83.49.11 problem Ex 11 page 127

Internal problem ID [19553]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 11 page 127
Date solved : Monday, March 31, 2025 at 07:33:10 PM
CAS classification : [_Lienard]

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

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

ode:=diff(diff(y(x),x),x)-2*tan(x)*diff(y(x),x)+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: 0.078 (sec). Leaf size: 51

ode=D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]+y[x]==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) - 2*tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False