90.23.11 problem 15

Internal problem ID [25364]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 365
Problem number : 15
Date solved : Friday, October 03, 2025 at 08:08:57 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y&=0 \end{align*}

Using Laplace method

✓ Maple. Time used: 0.069 (sec). Leaf size: 38

ode:=t*diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)+t*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t),method='laplace');
 

\[ y = \frac {\left (-\pi y \left (0\right )+2 c_1 \right ) \delta \left (t \right )}{2}+\frac {\sin \left (t \right ) y \left (0\right )+2 \left (-\cos \left (t \right )+1\right ) y^{\prime }\left (0\right )}{t} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 23

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

\begin{align*} y(t)&\to \frac {-c_3 \cos (t)+c_2 \sin (t)+c_1}{t} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(t), t) - (-t*Derivative(y(t), (t, 3)) - y(t) - 3*De