82.55.2 problem Ex. 2

Internal problem ID [19037]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter XI. Ordinary differential equations with more than two variables. problems at page 129
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:46:19 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 )&=0\\ \frac {d}{d t}y \left (t \right )-2 x \left (t \right )-5 y \left (t \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 47

dsolve([diff(x(t),t)-7*x(t)+y(t)=0,diff(y(t),t)-2*x(t)-5*y(t)=0],singsol=all)
 

\begin{align*} x &= {\mathrm e}^{6 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y &= -{\mathrm e}^{6 t} \left (c_{1} \cos \left (t \right )-c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right )-c_{2} \sin \left (t \right )\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 53

DSolve[{D[x[t],t]-7*x[t]+y[t]==0,D[y[t],t]-2*x[t]-5*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{6 t} (c_1 (\sin (t)+\cos (t))-c_2 \sin (t)) \\ y(t)\to e^{6 t} (c_2 \cos (t)+(2 c_1-c_2) \sin (t)) \\ \end{align*}