Internal problem ID [11015]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 3(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}\\ y^{\prime }\left (t \right )&=\frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2} \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 86
dsolve([diff(x(t),t)=5/4*x(t)+3/4*y(t),diff(y(t),t)=1/2*x(t)-3/2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {c_{1} {\mathrm e}^{\frac {\left (-1+\sqrt {145}\right ) t}{8}} \sqrt {145}}{4}-\frac {c_{2} {\mathrm e}^{-\frac {\left (1+\sqrt {145}\right ) t}{8}} \sqrt {145}}{4}+\frac {11 c_{1} {\mathrm e}^{\frac {\left (-1+\sqrt {145}\right ) t}{8}}}{4}+\frac {11 c_{2} {\mathrm e}^{-\frac {\left (1+\sqrt {145}\right ) t}{8}}}{4} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{\frac {\left (-1+\sqrt {145}\right ) t}{8}}+c_{2} {\mathrm e}^{-\frac {\left (1+\sqrt {145}\right ) t}{8}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 114
DSolve[{x'[t]==5/4*x[t]+3/4*y[t],y'[t]==1/2*x[t]-3/2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{145} e^{-t/8} \left (145 c_1 \cosh \left (\frac {\sqrt {145} t}{8}\right )+\sqrt {145} (11 c_1+6 c_2) \sinh \left (\frac {\sqrt {145} t}{8}\right )\right ) \\ y(t)\to \frac {1}{145} e^{-t/8} \left (145 c_2 \cosh \left (\frac {\sqrt {145} t}{8}\right )+\sqrt {145} (4 c_1-11 c_2) \sinh \left (\frac {\sqrt {145} t}{8}\right )\right ) \\ \end{align*}