Internal problem ID [1638]
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 3.
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 )&=-4 y_{1} \relax (t )+5 y_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 1.688 (sec). Leaf size: 58
dsolve([diff(y__1(t),t)=1*y__1(t)+2*y__2(t),diff(y__2(t),t)=-4*y__1(t)+5*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = \frac {{\mathrm e}^{3 t} \left (c_{1} \sin \left (2 t \right )+c_{2} \sin \left (2 t \right )-\cos \left (2 t \right ) c_{1}+c_{2} \cos \left (2 t \right )\right )}{2} \] \[ y_{2} \relax (t ) = {\mathrm e}^{3 t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 60
DSolve[{y1'[t]==1*y1[t]+2*y2[t],y2'[t]==-4*y1[t]+5*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{3 t} (c_1 \cos (2 t)+(c_2-c_1) \sin (2 t)) \\ \text {y2}(t)\to e^{3 t} (c_2 \cos (2 t)+(c_2-2 c_1) \sin (2 t)) \\ \end{align*}