7.19.3 problem 29

Internal problem ID [543]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.3 (Translation and partial fractions). Problems at page 296
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:54:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }-4 x&=3 t \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: 0.192 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)-4*x(t)=3*t,x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {3 t}{4}+\frac {3 \sinh \left (2 t \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 29

DSolve[{D[x[t],{t,2}]-4*x[t]==3*t,{x[0]==0,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {3}{16} e^{-2 t} \left (-4 e^{2 t} t+e^{4 t}-1\right ) \]