72.15.1 problem 3

Internal problem ID [14881]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 07:18:04 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve([diff(x(t),t)=3*x(t)+0*y(t),diff(y(t),t)=0*x(t)-2*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{3 t} \\ y &= c_{1} {\mathrm e}^{-2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 65

DSolve[{D[x[t],t]==3*x[t]+0*y[t],D[y[t],t]==0*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^{3 t} \\ y(t)\to c_2 e^{-2 t} \\ x(t)\to c_1 e^{3 t} \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^{-2 t} \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}