Internal problem ID [6363]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 72.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )-3 y \relax (t )\\ y^{\prime }\relax (t )&=3 x \relax (t )+7 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.06 (sec). Leaf size: 35
dsolve([diff(x(t),t)=x(t)-3*y(t),diff(y(t),t)=3*x(t)+7*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{4 t} \left (3 c_{2} t +3 c_{1}-c_{2}\right )}{3} \] \[ y \relax (t ) = {\mathrm e}^{4 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
DSolve[{x'[t]==x[t]-3*y[t],y'[t]==3*x[t]+7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{4 t} (-3 c_1 t-3 c_2 t+c_1) \\ y(t)\to e^{4 t} (3 (c_1+c_2) t+c_2) \\ \end{align*}