72.10.1 problem 1

Internal problem ID [14812]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 07:17:05 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: 0.033 (sec). Leaf size: 19

dsolve([diff(x(t),t)=3*x(t),diff(y(t),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: 0.002 (sec). Leaf size: 32

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

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