7.18.10 problem 10

Internal problem ID [539]
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 : 10
Date solved : Monday, January 27, 2025 at 02:54:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&=t \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.197 (sec). Leaf size: 21

dsolve([diff(x(t),t$2)+3*diff(x(t),t)+2*x(t)=t,x(0) = 0, D(x)(0) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {9 \,{\mathrm e}^{-2 t}}{4}+\frac {t}{2}-\frac {3}{4}+3 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 28

DSolve[{D[x[t],{t,2}]+3*D[x[t],t]+2*x[t]==t,{x[0]==0,Derivative[1][x][0] ==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} \left (2 t-9 e^{-2 t}+12 e^{-t}-3\right ) \]