79.3.2 problem 7 (ii)

Internal problem ID [18526]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 5. Linear equations. Exercises at page 85
Problem number : 7 (ii)
Date solved : Tuesday, January 28, 2025 at 11:51:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 20

dsolve([diff(x(t),t$2)-x(t)=exp(t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
 

\[ x = -\frac {{\mathrm e}^{-t}}{4}+\frac {\left (2 t +1\right ) {\mathrm e}^{t}}{4} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 27

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

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