52.10.2 problem 2

Internal problem ID [8396]
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 : 2
Date solved : Monday, January 27, 2025 at 03:57:29 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+2 y\\ y^{\prime }&=x \left (t \right )+3 y \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 30

dsolve([diff(x(t),t)=2*x(t)+2*y(t),diff(y(t),t)=x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{4 t} \\ y &= -\frac {c_{1} {\mathrm e}^{t}}{2}+c_{2} {\mathrm e}^{4 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 67

DSolve[{D[x[t],t]==2*x[t]+2*y[t],D[y[t],t]==x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^t \left (c_1 \left (e^{3 t}+2\right )+2 c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^t \left (c_1 \left (e^{3 t}-1\right )+c_2 \left (2 e^{3 t}+1\right )\right ) \\ \end{align*}