65.16.4 problem 29.3 (iv)

Internal problem ID [13841]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 29, Complex eigenvalues. Exercises page 292
Problem number : 29.3 (iv)
Date solved : Tuesday, January 28, 2025 at 06:04:58 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=7 x \left (t \right )-5 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=10 x \left (t \right )-3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 56

dsolve([diff(x(t),t)=7*x(t)-5*y(t),diff(y(t),t)=10*x(t)-3*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 62

DSolve[{D[x[t],t]==7*x[t]-5*y[t],D[y[t],t]==10*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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