Internal problem ID [11785]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=7 x \left (t \right )-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=10 x \left (t \right )-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 58
dsolve([diff(x(t),t)=7*x(t)-5*y(t),diff(y(t),t)=10*x(t)-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{2 t} \left (\sin \left (5 t \right ) c_{1} -\sin \left (5 t \right ) c_{2} +\cos \left (5 t \right ) c_{1} +\cos \left (5 t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{2 t} \left (\sin \left (5 t \right ) c_{1} +\cos \left (5 t \right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 62
DSolve[{x'[t]==7*x[t]-5*y[t],y'[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*}