76.24.4 problem 4

Internal problem ID [17732]
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 : 4
Date solved : Monday, March 31, 2025 at 04:26:10 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y&=\ln \left (t \right ) \end{align*}

✗ Maple

ode:=diff(diff(diff(y(t),t),t),t)+t*diff(diff(y(t),t),t)+5*t^2*diff(y(t),t)+2*t^3*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}]+5*t^2*D[y[t],t]+2*t^3*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(2*t**3*y(t) + 5*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) - (-2*t**3*y(t) - t*Derivative(y(t), (t, 2)) + log(t) - Derivative(y(t), (t, 3)))/(5*t**2) cannot be solved by the factorable group method