76.23.6 problem 7

Internal problem ID [17726]
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 6.1 (Definitions and examples). Problems at page 388
Problem number : 7
Date solved : Monday, March 31, 2025 at 04:26:04 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \end{align*}

✗ Maple

ode:=diff(diff(diff(y(t),t),t),t)+t*diff(diff(y(t),t),t)+t^2*diff(y(t),t)+t^2*y(t) = ln(t); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,3}]+t*D[y[t],{t,2}]+t^2*D[y[t],t]+t^2*y[t]==Log[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**2*y(t) + t**2*Derivative(y(t), t) + t*Derivative(y(t), (t, 2)) - log(t) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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