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Program 1
Solve ODE using scipy.integrate.odeint()
The differential equation is: $$ \frac{dx}{dt} = -k \cdot x $$ $$ x(t = 0) = 10 $$
Output 1
Program 2
Solve ODE using scipy.integrate.odeint()
The ordinary differential equation (ODE) given by:
\[ \frac{dx}{dt} = -k \cdot x, \] where \( x(t) \) is a function of time \( t \) and \( k \) is a positive constant. Consider three different values of \( k \): \( k = 0.5, 1, 2.5 \) over the time interval \( t = [0, 10] \) with the initial condition \( x(0) = 10.0 \).Output 2
Program 3
Solve ODE using scipy.integrate.odeint()
The differential equation is: $$ \frac{d^2x}{dt^2} + \lambda \frac{dx}{dt} + kx = 0 $$ $$ x_{t=0} = 0 \quad \text{and} \quad \left. \frac{dx}{dt} \right|_{t=0} = 0.7$$
Output 3