Internal problem ID [1636]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.6, constant coefficient
homogeneous system III. Page 566
Problem number: section 10.6, problem 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-y_{1}\relax (t )+2 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-5 y_{1}\relax (t )+5 y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 48
dsolve([diff(y__1(t),t)=-1*y__1(t)+2*y__2(t),diff(y__2(t),t)=-5*y__1(t)+5*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = \frac {{\mathrm e}^{2 t} \left (3 c_{1} \sin \relax (t )+\sin \relax (t ) c_{2}-\cos \relax (t ) c_{1}+3 c_{2} \cos \relax (t )\right )}{5} \] \[ y_{2}\relax (t ) = {\mathrm e}^{2 t} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 55
DSolve[{y1'[t]==-1*y1[t]+2*y2[t],y2'[t]==-5*y1[t]+5*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{2 t} (c_1 \cos (t)+(2 c_2-3 c_1) \sin (t)) \\ \text {y2}(t)\to e^{2 t} (c_2 (3 \sin (t)+\cos (t))-5 c_1 \sin (t)) \\ \end{align*}