63.18.4 problem 2(d)

Internal problem ID [13210]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 190
Problem number : 2(d)
Date solved : Tuesday, January 28, 2025 at 05:12:28 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=4 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.990 (sec). Leaf size: 22

dsolve([diff(x(t),t)=4*y(t),diff(y(t),t)=2*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 65

DSolve[{D[x[t],t]==4*x[t],D[y[t],t]==2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^{4 t} \\ y(t)\to c_2 e^{2 t} \\ x(t)\to c_1 e^{4 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*}