7.18.8 problem 8

Internal problem ID [537]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 8
Date solved : Wednesday, February 05, 2025 at 03:42:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+9 x&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.194 (sec). Leaf size: 12

dsolve([diff(x(t),t$2)+9*x(t)=1,x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {\cos \left (3 t \right )}{9}+\frac {1}{9} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 17

DSolve[{D[x[t],{t,2}]+9*x[t]==1,{x[0]==0,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2}{9} \sin ^2\left (\frac {3 t}{2}\right ) \]