10.17.3 problem 3

Internal problem ID [1418]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.8, Repeated Eigenvalues. page 436
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:57:02 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-\frac {3 x_{1} \left (t \right )}{2}+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-\frac {x_{1} \left (t \right )}{4}-\frac {x_{2} \left (t \right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 31

dsolve([diff(x__1(t),t)=-3/2*x__1(t)+1*x__2(t),diff(x__2(t),t)=-1/4*x__1(t)-1/2*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_2 t +c_1 \right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (c_2 t +c_1 +2 c_2 \right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 54

DSolve[{D[ x1[t],t]==-3/2*x1[t]+1*x2[t],D[ x2[t],t]==-1/4*x1[t]-1/2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} (2 c_2 t-c_1 (t-2)) \\ \text {x2}(t)\to \frac {1}{4} e^{-t} (c_1 (-t)+2 c_2 t+4 c_2) \\ \end{align*}