Internal problem ID [12537]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 171.
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 )&=x \left (t \right )-y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(x(t),t) = x(t)-2*y(t), diff(y(t),t) = x(t)-y(t), x(0) = 1, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= -\sin \left (t \right )+\cos \left (t \right ) \\ y \left (t \right ) &= \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 17
DSolve[{x'[t]==x[t]-2*y[t],y'[t]==x[t]-y[t]},{x[0]==1,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \cos (t)-\sin (t) \\ y(t)\to \cos (t) \\ \end{align*}