71.19.2 problem 2

Internal problem ID [14594]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:44:02 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-x \left (t \right )+2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right )+3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

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

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