74.22.13 problem 13

Internal problem ID [16660]
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 : 13
Date solved : Tuesday, January 28, 2025 at 09:16:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-3 x^{\prime }+4 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

\[ x \left (t \right ) = {\mathrm e}^{\frac {3 t}{2}} \left (c_{1} \sin \left (\frac {\sqrt {7}\, t}{2}\right )+c_{2} \cos \left (\frac {\sqrt {7}\, t}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 42

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

\[ x(t)\to e^{3 t/2} \left (c_2 \cos \left (\frac {\sqrt {7} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} t}{2}\right )\right ) \]