11.1.9 problem 20

Internal problem ID [1470]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number : 20
Date solved : Thursday, March 13, 2025 at 04:47:37 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 16

ode:=(-t+2)*diff(diff(diff(y(t),t),t),t)+(2*t-3)*diff(diff(y(t),t),t)-t*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_3 t +c_2 \right ) {\mathrm e}^{t}+c_1 t \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 28

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

\[ y(t)\to t \left (c_2 e^t+c_1\right )+(c_3-4 c_2) e^t \]

✗ Sympy

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

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