Internal problem ID [12234]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 196.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )-x \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )-3 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (1\right ) = 0, y \left (1\right ) = 1] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve([diff(x(t),t) = y(t)-x(t), diff(y(t),t) = -x(t)-3*y(t), x(1) = 0, y(1) = 1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-2 t} \left (-{\mathrm e}^{2} t +{\mathrm e}^{2}\right ) \] \[ y \left (t \right ) = {\mathrm e}^{-2 t} \left (-{\mathrm e}^{2} t +2 \,{\mathrm e}^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[{x'[t]==y[t]-x[t],y'[t]==-x[t]-3*y[t]},{x[1]==0,y[1]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2-2 t} (t-1) y(t)\to -e^{2-2 t} (t-2) \end{align*}