Internal problem ID [12216]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 170.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )+1\\ y^{\prime }\left (t \right )&=x \left (t \right )+1 \end {align*}
With initial conditions \[ [x \left (0\right ) = -2, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 22
dsolve([diff(x(t),t) = y(t)+1, diff(y(t),t) = x(t)+1, x(0) = -2, y(0) = 0],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -1-{\mathrm e}^{-t} \] \[ y \left (t \right ) = -1+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 24
DSolve[{x'[t]==y[t]+1,y'[t]==x[t]+1},{x[0]==-2,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{-t}-1 y(t)\to e^{-t}-1 \end{align*}