56.1.75 problem 75

Internal problem ID [8787]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 75
Date solved : Monday, January 27, 2025 at 04:58:38 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 26

dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=y(t),diff(z(t),t)=z(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \left (c_{2} t +c_{1} \right ) {\mathrm e}^{t} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ z \left (t \right ) &= c_3 \,{\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 62

DSolve[{D[x[t],t]== x[t]+y[t],D[y[t],t] == y[t],D[z[t],t]==z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^t (c_2 t+c_1) \\ y(t)\to c_2 e^t \\ z(t)\to c_3 e^t \\ x(t)\to e^t (c_2 t+c_1) \\ y(t)\to c_2 e^t \\ z(t)\to 0 \\ \end{align*}