Internal problem ID [5777]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section A. Drill exercises. Page
400
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=4 x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 36
dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=4*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {c_{1} {\mathrm e}^{-t}}{2}+\frac {{\mathrm e}^{3 t} c_{2}}{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-t}+{\mathrm e}^{3 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 51
DSolve[{x'[t]==x[t]+y[t],y'[t]==4*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^t (2 c_1 \cosh (2 t)+c_2 \sinh (2 t)) \\ y(t)\to e^t (c_2 \cosh (2 t)+2 c_1 \sinh (2 t)) \\ \end{align*}