7.20.3 problem 31

Internal problem ID [557]
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 : 31
Date solved : Monday, January 27, 2025 at 02:54:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) 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)-(4*t+1)*diff(x(t),t)+2*(2*t+1)*x(t)=0,x(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{2} {\mathrm e}^{2 t} c_1}{2} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 19

DSolve[{t*D[x[t],{t,2}]-(4*t+1)*D[x[t],t]+2*(2*t+1)*x[t]==0,{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} c_2 e^{2 t} t^2 \]