10.18.11 problem 11

Internal problem ID [1438]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:57:19 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 56

dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t)+0,diff(x__2(t),t)=1*x__1(t)-2*x__2(t)+cos(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= \sin \left (t \right ) c_2 +\cos \left (t \right ) c_1 -\frac {5 \sin \left (t \right ) t}{2} \\ x_{2} \left (t \right ) &= -\frac {c_2 \cos \left (t \right )}{5}+\frac {c_1 \sin \left (t \right )}{5}+\frac {\cos \left (t \right ) t}{2}+\frac {\sin \left (t \right )}{2}+\frac {2 \sin \left (t \right ) c_2}{5}+\frac {2 \cos \left (t \right ) c_1}{5}-\sin \left (t \right ) t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 60

DSolve[{D[ x1[t],t]==2*x1[t]-5*x2[t]+0,D[ x2[t],t]==1*x1[t]-2*x2[t]-Cos[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \left (\frac {5}{2}+c_1\right ) \cos (t)+\frac {1}{2} (5 t+4 c_1-10 c_2) \sin (t) \\ \text {x2}(t)\to \left (-\frac {t}{2}+1+c_2\right ) \cos (t)+(t+c_1-2 c_2) \sin (t) \\ \end{align*}