75.29.3 problem 804

Internal problem ID [17257]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous linear systems with constant coefficients. Eulers method. Exercises page 230
Problem number : 804
Date solved : Tuesday, January 28, 2025 at 09:58:30 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-3 y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

\begin{align*} x \left (t \right ) &= 0 \\ y \left (t \right ) &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 10

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

\begin{align*} x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}