7.20.1 problem 29

Internal problem ID [555]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.4 (Derivatives, Integrals and products of transforms). Problems at page 303
Problem number : 29
Date solved : Saturday, March 29, 2025 at 04:56:33 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.094 (sec). Leaf size: 14

ode:=t*diff(diff(x(t),t),t)+(t-2)*diff(x(t),t)+x(t) = 0; 
ic:=x(0) = 0; 
dsolve([ode,ic],x(t),method='laplace');
 

\[ x = \frac {c_1 \,t^{3} {\mathrm e}^{-t}}{6} \]

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 16

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

\[ x(t)\to c_1 e^{-t} t^3 \]

✗ Sympy

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

ValueError : Couldnt solve for initial conditions