Internal problem ID [6522]
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 10.3 Homogeneous Linear
Systems with Constant Coefficients. Page 387
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=-x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==-x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} (2 c_1 t+4 c_2 t+c_1) \\ y(t)\to e^{3 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}