79.2.2 problem 2

Internal problem ID [18515]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 4. Autonomous systems. Exercises at page 69
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 11:51:39 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.290 (sec). Leaf size: 23

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

\begin{align*} x &= c_{2} {\mathrm e}^{t} \\ y &= -c_{2} {\mathrm e}^{t}+c_{1} {\mathrm e}^{2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 33

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

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