54.9.1 problem 1856

Internal problem ID [13079]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1856
Date solved : Wednesday, October 01, 2025 at 03:34:18 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.098 (sec). Leaf size: 18

ode:=[diff(x(t),t) = a*x(t), diff(y(t),t) = b]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{a t} \\ y \left (t \right ) &= b t +c_2 \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 36

ode={D[x[t],t]==a*x[t],D[y[t],t]==b}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{a t}\\ y(t)&\to b t+c_2\\ x(t)&\to 0\\ y(t)&\to b t+c_2 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 15

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

\[ \left [ x{\left (t \right )} = C_{1} e^{a t}, \ y{\left (t \right )} = C_{2} + b t\right ] \]