56.1.74 problem 74

Internal problem ID [8786]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 74
Date solved : Monday, January 27, 2025 at 04:58:37 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=7 x \left (t \right )+y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-4 x \left (t \right )+3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 34

dsolve([diff(x(t),t) = 7*x(t)+y(t), diff(y(t),t) = -4*x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -{\mathrm e}^{5 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 45

DSolve[{D[x[t],t]== 7*x[t]+y[t],D[y[t],t] == -4*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{5 t} (2 c_1 t+c_2 t+c_1) \\ y(t)\to e^{5 t} (c_2-2 (2 c_1+c_2) t) \\ \end{align*}