ODE solver methods (RK45, BDF) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the ODE solver function from scipy.

SciPy

from scipy.integrate import [1]

Drag options to blanks, or click blank then click option'

Aodeint

Bode

Csolve_ivp

Dintegrate

Attempts:

3 left

💡 Hint

Common Mistakes

Using odeint which is older and less flexible.

Trying to import a non-existent function.

The solve_ivp function is the modern ODE solver in scipy that supports methods like RK45 and BDF.

2fill in blank

medium

Complete the code to define the ODE function for dy/dt = -2y.

SciPy

def dydt(t, y):
    return [1] * y

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A2

B-2

C-y

Dy

Attempts:

3 left

💡 Hint

Common Mistakes

Returning just -y instead of -2*y.

Returning a positive 2 instead of negative.

The ODE is dy/dt = -2y, so the function returns -2 times y.

3fill in blank

hard

Fix the error in the code to solve the ODE using RK45 method.

SciPy

sol = solve_ivp(dydt, [0, 5], [1], method=[1])

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A"bdf"

B"euler"

C"rk45"

D"RK45"

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase 'rk45' which causes an error.

Using unsupported method names like 'euler'.

The method name is case-sensitive and should be "RK45" with uppercase letters.

4fill in blank

hard

Fill both blanks to solve the ODE using BDF method and print the solution at t=5.

SciPy

sol = solve_ivp(dydt, [0, [1]], [1], method=[2])
print(sol.y[0, -1])

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A5

B10

C"RK45"

D"BDF"

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong end time like 10.

Using lowercase method names.

The time interval ends at 5, and the method for stiff problems is "BDF".

5fill in blank

hard

Fill all three blanks to create a dictionary of solutions at specific times using RK45 method.

SciPy

times = [0, 1, 2, 3]
sol = solve_ivp(dydt, [0, 3], [1], method=[1], t_eval=[2])
results = {t: y for t, y in zip(sol.t, sol.y[0]) if t [3] 0}

Drag options to blanks, or click blank then click option'

A"RK45"

B[0, 1, 2, 3]

C>=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Not passing t_eval to get solution at specific times.

Using wrong comparison operator in dictionary comprehension.

Use "RK45" as method, provide t_eval as the list of times, and filter times greater or equal to 0.