Basics of Differential Equations

What a differential equation is

Verifying and the general solution

Where differential equations come from

A first table of solutions

The equation y double prime plus y = 0 is classified as what order?

Which of the following differential equations is linear?

To verify that y = C e^(2x) solves y prime = 2y, what does one do?

In the initial value problem y prime = ky with y(0) = 5, what does the condition contribute?

The existence and uniqueness theorem for y prime = f(x, y) with y(x_0) = y_0 guarantees what, when f is well-behaved?

A second order differential equation's general solution contains how many arbitrary constants? Answer with a number.

In a differential equation like y prime = ky, the unknown being solved for is what kind of mathematical object?

The logistic equation dP/dt = kP(1 - P/K) involves only the first derivative of P. What order is it? Answer with a number.

For y prime = 3y with y(0) = 2, the particular solution is 2 e^(3x). At x = 0, what value does it take? Answer with a number.

The pendulum equation theta double prime plus sin theta = 0 is nonlinear because of which function applied to the unknown? Answer with the function name in lowercase.