69.1.120 problem 171

Internal problem ID [14273]
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
Date solved : Tuesday, January 28, 2025 at 06:25:14 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 1 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 16

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 ) &= \cos \left (t \right )-\sin \left (t \right ) \\ y \left (t \right ) &= \cos \left (t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 17

DSolve[{D[x[t],t]==x[t]-2*y[t],D[y[t],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*}