52.10.31 problem 34

Internal problem ID [8425]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.2. Page 346
Problem number : 34
Date solved : Monday, January 27, 2025 at 04:00:21 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=x \left (t \right )+y\\ y^{\prime }&=-2 x \left (t \right )-y \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 36

dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=-2*x(t)-y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right ) \\ y &= \cos \left (t \right ) c_{1} -c_{2} \sin \left (t \right )-c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 39

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

\begin{align*} x(t)\to c_1 \cos (t)+(c_1+c_2) \sin (t) \\ y(t)\to c_2 \cos (t)-(2 c_1+c_2) \sin (t) \\ \end{align*}