Internal problem ID [10542]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 237
Problem number: 4(f).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 54
dsolve([diff(x(t),t)=3*x(t)-2*y(t),diff(y(t),t)=4*x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{t} \left (\cos \left (2 t \right ) c_{1} +c_{2} \cos \left (2 t \right )+c_{1} \sin \left (2 t \right )-\sin \left (2 t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 58
DSolve[{x'[t]==3*x[t]-2*y[t],y'[t]==4*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cos (2 t)+(c_1-c_2) \sin (2 t)) \\ y(t)\to e^t (c_2 \cos (2 t)+(2 c_1-c_2) \sin (2 t)) \\ \end{align*}