76.12.4 problem 4

Internal problem ID [17489]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 4
Date solved : Monday, March 31, 2025 at 04:15:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=3\\ y^{\prime }\left (2\right )&=1 \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+cos(t)*diff(y(t),t)+3*ln(t)*y(t) = 0; 
ic:=y(2) = 3, D(y)(2) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+Cos[t]*D[y[t],t]+3*Log[t]*y[t]==0; 
ic={y[2]==3,Derivative[1][y][2]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t)*log(t) + cos(t)*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(2): 3, Subs(Derivative(y(t), t), t, 2): 1} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -(-3*y(t)*log(t) - Derivative(y(t), (t, 2)))/cos(t) + Derivative(y(t), t) cannot be solved by the factorable group method