69.1.134 problem 193

Internal problem ID [14287]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 193
Date solved : Tuesday, January 28, 2025 at 06:25:46 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=12 x \left (t \right )+18 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-8 x \left (t \right )-12 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 23

dsolve([diff(x(t),t)=12*x(t)+18*y(t),diff(y(t),t)=-8*x(t)-12*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} t +c_{2} \\ y \left (t \right ) &= \frac {1}{18} c_{1} -\frac {2}{3} c_{1} t -\frac {2}{3} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 36

DSolve[{D[x[t],t]==12*x[t]+18*y[t],D[y[t],t]==-8*x[t]-12*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 12 c_1 t+18 c_2 t+c_1 \\ y(t)\to c_2-4 (2 c_1+3 c_2) t \\ \end{align*}