10.18.8 problem 8

Internal problem ID [1435]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number : 8
Date solved : Monday, January 27, 2025 at 04:57:16 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 44

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

\begin{align*} x_{1} \left (t \right ) &= c_2 \,{\mathrm e}^{t}+{\mathrm e}^{-t} c_1 +2 t \,{\mathrm e}^{t} \\ x_{2} \left (t \right ) &= c_2 \,{\mathrm e}^{t}+3 \,{\mathrm e}^{-t} c_1 -{\mathrm e}^{t}+2 t \,{\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 80

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

\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (e^{2 t} (4 t-1+3 c_1-c_2)-c_1+c_2\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (e^{2 t} (4 t-3+3 c_1-c_2)-3 c_1+3 c_2\right ) \\ \end{align*}