76.24.2 problem 2

Internal problem ID [17730]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 2
Date solved : Monday, March 31, 2025 at 04:26:08 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \end{align*}

✗ Maple

ode:=t*diff(diff(diff(y(t),t),t),t)+sin(t)*diff(diff(y(t),t),t)+4*y(t) = cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=t*D[y[t],{t,3}]+Sin[t]*D[y[t],{t,2}]+4*y[t]==Cos[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), (t, 3)) + 4*y(t) + sin(t)*Derivative(y(t), (t, 2)) - cos(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve t*Derivative(y(t), (t, 3)) + 4*y(t) + sin(t)*Derivative(y(t), (t, 2)) - cos(t)