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 : Monday, January 27, 2025 at 02:54:47 AM
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*}

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 14

dsolve([t*diff(x(t),t$2)+(t-2)*diff(x(t),t)+x(t)=0,x(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{3} {\mathrm e}^{-t} c_1}{6} \]

✓ Solution by Mathematica

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

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

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