74.22.16 problem 16

Internal problem ID [16663]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 09:16:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(diff(x(t),t$2)+x(t)=exp(t),x(t), singsol=all)
 

\[ x \left (t \right ) = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} +\frac {{\mathrm e}^{t}}{2} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 53

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

\[ x(t)\to \cos (t) \int _1^t-e^{K[1]} \sin (K[1])dK[1]+\sin (t) \int _1^te^{K[2]} \cos (K[2])dK[2]+c_1 \cos (t)+c_2 \sin (t) \]