69.1.119 problem 170

Internal problem ID [14272]
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
Date solved : Tuesday, January 28, 2025 at 06:25:13 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=y \left (t \right )+1\\ \frac {d}{d t}y \left (t \right )&=1+x \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = -2\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 21

dsolve([diff(x(t),t) = y(t)+1, diff(y(t),t) = x(t)+1, x(0) = -2, y(0) = 0], singsol=all)
 

\begin{align*} x \left (t \right ) &= -{\mathrm e}^{-t}-1 \\ y \left (t \right ) &= {\mathrm e}^{-t}-1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 24

DSolve[{D[x[t],t]==y[t]+1,D[y[t],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*}