ODE solvers (ode45) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to solve the ODE dy/dt = -2y using ode45.

MATLAB

tspan = [0 5]; y0 = 1;
[t, y] = ode45(@(t,y) [1], tspan, y0);

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

A-2*y

B2*y

Cy-2

Dt*y

Attempts:

3 left

💡 Hint

Common Mistakes

Using '2*y' instead of '-2*y' changes the sign and the solution behavior.

Writing 'y-2' or 't*y' does not represent the given ODE.

The function inside ode45 defines the derivative dy/dt = -2*y.

2fill in blank

medium

Complete the code to plot the solution y versus time t.

MATLAB

plot(t, [1]);
xlabel('Time'); ylabel('Solution y');

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

Ay0

Bt

Ctspan

Dy

Attempts:

3 left

💡 Hint

Common Mistakes

Plotting t against t or tspan does not show the solution.

Using y0 plots only the initial value, not the solution.

We plot the solution values y against time t.

3fill in blank

hard

Fix the error in the function definition for ode45 to solve dy/dt = y^2 - t.

MATLAB

odefun = @(t,y) [1];
[t, y] = ode45(odefun, [0 2], 0.5);

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

Ay^2 - y

By**2 - t

Cy^2 - t

Dt - y^2

Attempts:

3 left

💡 Hint

Common Mistakes

Using '**' causes syntax errors in MATLAB.

Changing the equation changes the problem.

In MATLAB, '^' is used for power, so 'y^2 - t' is correct.

4fill in blank

hard

Fill both blanks to create a function handle for dy/dt = sin(t) - y.

MATLAB

odefun = @(t, y) [1] - [2];
[t, y] = ode45(odefun, [0 10], 1);

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

Asin(t)

Bcos(t)

Cy

Dt

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'cos(t)' instead of 'sin(t)' changes the equation.

Using 't' instead of 'y' changes the dependent variable.

The derivative is dy/dt = sin(t) - y, so the function is 'sin(t) - y'.

5fill in blank

hard

Fill all three blanks to solve dy/dt = -3y + 2t and plot the result.

MATLAB

odefun = @(t, y) [1] * [2] + 2 * [3];
[t, y] = ode45(odefun, [0 4], 0);
plot(t, y);

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

A-3

By

Ct

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up variables y and t.

Using wrong coefficients changes the equation.

The function is dy/dt = -3*y + 2*t, so blanks are '-3', 'y', and 't'.