90.23.3 problem 7

Internal problem ID [25356]
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 : 7
Date solved : Friday, October 03, 2025 at 12:00:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \end{align*}

Using Laplace method

✓ Maple. Time used: 0.040 (sec). Leaf size: 11

ode:=t*diff(diff(y(t),t),t)+(2+4*t)*diff(y(t),t)+(4+4*t)*y(t) = 0; 
dsolve(ode,y(t),method='laplace');
 

\[ y = y \left (0\right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

ode=t*D[y[t],{t,2}]+(2+4*t)*D[y[t],t]+(4+4*t)*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {e^{-2 t} (c_2 t+c_1)}{t} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), (t, 2)) + (4*t + 2)*Derivative(y(t), t) + (4*t + 4)*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

False