Internal problem ID [6005]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.2. Page 346
Problem number: 35.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=5 x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )+3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.05 (sec). Leaf size: 46
dsolve([diff(x(t),t)=5*x(t)+y(t),diff(y(t),t)=-2*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{4 t} \left (\cos \relax (t ) c_{1}+c_{2} \cos \relax (t )+\sin \relax (t ) c_{1}-\sin \relax (t ) c_{2}\right )}{2} \] \[ y \relax (t ) = {\mathrm e}^{4 t} \left (c_{2} \cos \relax (t )+\sin \relax (t ) c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 51
DSolve[{x'[t]==5*x[t]+y[t],y'[t]==-2*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{4 t} (c_1 \cos (t)+(c_1+c_2) \sin (t)) \\ y(t)\to e^{4 t} (c_2 \cos (t)-(2 c_1+c_2) \sin (t)) \\ \end{align*}