Internal problem ID [13082]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+4 y\\ y^{\prime }&=x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(x(t),t)=3*x(t)+4*y(t),diff(y(t),t)=1*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= 4 c_{1} {\mathrm e}^{4 t}-c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 71
DSolve[{x'[t]==3*x[t]+4*y[t],y'[t]==1*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (4 e^{5 t}+1\right )+4 c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (e^{5 t}-1\right )+c_2 \left (e^{5 t}+4\right )\right ) \\ \end{align*}