7.20.5 problem 33

Internal problem ID [559]
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 : 33
Date solved : Monday, January 27, 2025 at 02:54:48 AM
CAS classification : [_Lienard]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.197 (sec). Leaf size: 16

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

\[ x \left (t \right ) = -\frac {c_1 \left (\cos \left (t \right ) t -\sin \left (t \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 27

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

\[ x(t)\to -\sqrt {\frac {2}{\pi }} c_1 (t \cos (t)-\sin (t)) \]