58.2.49 problem 49

Internal problem ID [9172]
Book : Second order enumerated odes
Section : section 2
Problem number : 49
Date solved : Monday, January 27, 2025 at 05:51:42 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

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

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