11.1.10 problem 21

Internal problem ID [1471]
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 : 21
Date solved : Saturday, March 29, 2025 at 10:55:59 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

ode:=t^2*(t+3)*diff(diff(diff(y(t),t),t),t)-3*t*(t+2)*diff(diff(y(t),t),t)+6*(1+t)*diff(y(t),t)-6*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_2 \,t^{3}+c_1 \,t^{2}+c_3 t +c_3 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 58

ode=t^2*(t+3)*D[ y[t],{t,3}]-3*t*(t+2)*D[y[t],{t,2}]+6*(1+t)*D[y[t],t]-6*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{8} \left (2 c_1 \left (t^3-3 t^2+3 t+3\right )-(t-1) \left (4 c_2 \left (t^2-2 t-1\right )+c_3 \left (-3 t^2+2 t+1\right )\right )\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*(t + 3)*Derivative(y(t), (t, 3)) - 3*t*(t + 2)*Derivative(y(t), (t, 2)) + (6*t + 6)*Derivative(y(t), t) - 6*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - (-t**3*Derivative(y(t), (t, 3))/6 + t**2*Derivative(y(t), (t, 2))/2 - t**2*Derivative(y(t), (t, 3))/2 + t*Derivative(y(t), (t, 2)) + y(t))/(t + 1) cannot be solved by the factorable group method