What is a differential equation?
What is the general solution to dy/dx = ky?
Hint: This models population growth and radioactive decay
What is separation of variables?
What is a slope field?
What is an initial value problem?
What real-world situation does dy/dt = -ky model?
How do you verify that a given function y = f(x) is a solution to a differential equation?
Hint: Plug the candidate solution and its derivative back into the original equation
Solve the separable differential equation dy/dx = 2x, y(0) = 3.
Hint: Integrate both sides, then use the initial condition to find the constant
In a slope field, what does it mean if the line segments at every point with the same y-value are parallel?
Hint: Segments with the same y-value are on a horizontal line — what stays constant along that line?
A cup of coffee cools according to Newton's Law of Cooling, dT/dt = -k(T - Tₐ). What does Tₐ represent?
Hint: The coffee cools toward the temperature of the room around it
Solve the separable equation dy/dx = y/x for x > 0, y > 0.
Hint: Separate variables to get dy/y = dx/x, then integrate both sides
What order is the differential equation d²y/dx² + 3(dy/dx) - y = 0?
Hint: The order of a differential equation is determined by its highest derivative