Internal problem ID [13079]
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: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y\\ y^{\prime }&=-x \left (t \right )+4 y \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve([diff(x(t),t)=2*x(t)+1*y(t),diff(y(t),t)=-x(t)+4*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 ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} +c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[{x'[t]==2*x[t]+1*y[t],y'[t]==-x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} (c_1 (-t)+c_2 t+c_1) \\ y(t)\to e^{3 t} ((c_2-c_1) t+c_2) \\ \end{align*}