76.52.3 problem Ex. 3

Internal problem ID [20296]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 116
Problem number : Ex. 3
Date solved : Thursday, October 02, 2025 at 05:41:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*tan(x)*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sec \left (x \right ) \left (c_1 \sin \left (\sqrt {6}\, x \right )+c_2 \cos \left (\sqrt {6}\, x \right )\right ) \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 49

ode=D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (c_1 e^{-i \sqrt {6} x}-\frac {i c_2 e^{i \sqrt {6} x}}{2 \sqrt {6}}\right ) \sec (x) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 2*tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False