72.9.3 problem 3

Internal problem ID [14799]
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 3.1. page 258
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 07:15:54 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 26

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

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