Internal problem ID [12538]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-x(t)+2*y(t),diff(y(t),t)=-2*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[{x'[t]==-x[t]+2*y[t],y'[t]==-2*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (-2 c_1 t+2 c_2 t+c_1) y(t)\to e^t (-2 c_1 t+2 c_2 t+c_2) \end{align*}