Internal problem ID [5959]
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 8.1. Page 332
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=4 x \relax (t )-7 y \relax (t )\\ y^{\prime }\relax (t )&=5 x \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 78
dsolve([diff(x(t),t)=4*x(t)-7*y(t),diff(y(t),t)=5*x(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{2 t} \left (\sqrt {31}\, \sin \left (\sqrt {31}\, t \right ) c_{2}-\sqrt {31}\, \cos \left (\sqrt {31}\, t \right ) c_{1}-2 \sin \left (\sqrt {31}\, t \right ) c_{1}-2 \cos \left (\sqrt {31}\, t \right ) c_{2}\right )}{5} \] \[ y \relax (t ) = {\mathrm e}^{2 t} \left (\sin \left (\sqrt {31}\, t \right ) c_{1}+\cos \left (\sqrt {31}\, t \right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 98
DSolve[{x'[t]==4*x[t]-7*y[t],y'[t]==5*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{2 t} \cos \left (\sqrt {31} t\right )+\frac {(2 c_1-7 c_2) e^{2 t} \sin \left (\sqrt {31} t\right )}{\sqrt {31}} \\ y(t)\to c_2 e^{2 t} \cos \left (\sqrt {31} t\right )+\frac {(5 c_1-2 c_2) e^{2 t} \sin \left (\sqrt {31} t\right )}{\sqrt {31}} \\ \end{align*}