Internal problem ID [6365]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 74.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=7 x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=-4 x \relax (t )+3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 33
dsolve([diff(x(t),t) = 7*x(t)+y(t), diff(y(t),t) = -4*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{5 t} \left (2 t c_{2}+2 c_{1}+c_{2}\right )}{4} \] \[ y \relax (t ) = {\mathrm e}^{5 t} \left (t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 45
DSolve[{x'[t]== 7*x[t]+y[t],y'[t] == -4*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{5 t} (2 c_1 t+c_2 t+c_1) \\ y(t)\to e^{5 t} (c_2-2 (2 c_1+c_2) t) \\ \end{align*}