69.1.134 problem 193

Internal problem ID [14216]
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 : Monday, March 31, 2025 at 12:12:57 PM
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*}

✓ Maple. Time used: 0.083 (sec). Leaf size: 23

ode:=[diff(x(t),t) = 12*x(t)+18*y(t), diff(y(t),t) = -8*x(t)-12*y(t)]; 
dsolve(ode);
 

\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*}

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

ode={D[x[t],t]==12*x[t]+18*y[t],D[y[t],t]==-8*x[t]-12*y[t]}; 
ic={}; 
DSolve[{ode,ic},{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*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-12*x(t) - 18*y(t) + Derivative(x(t), t),0),Eq(8*x(t) + 12*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = 12 C_{1} t + C_{1} + 12 C_{2}, \ y{\left (t \right )} = - 8 C_{1} t - 8 C_{2}\right ] \]