Question 1
Which of the following first-order ODEs can be solved by direct integration after rearrangement?
Question 2
What is the primary characteristic that distinguishes a linear first-order ODE from a non-linear first-order ODE?
Question 3
When solving a separable differential equation of the form $\frac{dy}{dx} = f(x)g(y)$, what is the first step?
Question 4
Which of the following is a necessary condition for a first-order ODE $\frac{dy}{dx} = f(x,y)$ to be classified as an exact differential equation?
Question 5
Consider the ODE $(3x^2 + 2xy)dx + (x^2 + 2y)dy = 0$. To determine if it is exact, what partial derivatives need to be calculated and compared?
