10.15.1 problem 30

Internal problem ID [1400]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.5, Homogeneous Linear Systems with Constant Coefficients. page 407
Problem number : 30
Date solved : Monday, January 27, 2025 at 04:56:46 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-\frac {x_{1} \left (t \right )}{10}+\frac {3 x_{2} \left (t \right )}{40}\\ \frac {d}{d t}x_{2} \left (t \right )&=\frac {x_{1} \left (t \right )}{10}-\frac {x_{2} \left (t \right )}{5} \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = -17\\ x_{2} \left (0\right ) = -21 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 33

dsolve([diff(x__1(t),t) = -1/10*x__1(t)+3/40*x__2(t), diff(x__2(t),t) = 1/10*x__1(t)-1/5*x__2(t), x__1(0) = -17, x__2(0) = -21], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= -\frac {165 \,{\mathrm e}^{-\frac {t}{20}}}{8}+\frac {29 \,{\mathrm e}^{-\frac {t}{4}}}{8} \\ x_{2} \left (t \right ) &= -\frac {55 \,{\mathrm e}^{-\frac {t}{20}}}{4}-\frac {29 \,{\mathrm e}^{-\frac {t}{4}}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

DSolve[{D[ x1[t],t]==-1/10*x1[t]+3/40*x2[t],D[ x2[t],t]==1/10*x1[t]-1/5*x2[t]},{x1[0]==-17,x2[0]==-21},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{8} e^{-t/4} \left (29-165 e^{t/5}\right ) \\ \text {x2}(t)\to -\frac {1}{4} e^{-t/4} \left (55 e^{t/5}+29\right ) \\ \end{align*}