67.2.28 problem Problem 5(b)

Internal problem ID [13914]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 5(b)
Date solved : Monday, March 31, 2025 at 08:17:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=1\\ y^{\prime }\left (\frac {\pi }{4}\right )&=0 \end{align*}

✓ Maple. Time used: 8.035 (sec). Leaf size: 1300

ode:=diff(diff(y(x),x),x)+tan(x)*diff(y(x),x)+cot(x)*y(x) = 0; 
ic:=y(1/4*Pi) = 1, D(y)(1/4*Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=D[y[x],{x,2}]+Tan[x]*D[y[x],x]+Cot[x]*y[x]==0; 
ic={y[Pi/4]==1,Derivative[1][y][Pi/4]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)/tan(x) + tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(pi/4): 1, Subs(Derivative(y(x), x), x, pi/4): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE (y(x)/tan(x) + Derivative(y(x), (x, 2)))/tan(x) + Derivative(y(x), x) cannot be solved by the factorable group method