First-Order Linear Equations

Standard form and the integrating factor

The homogeneous-plus-particular structure

Initial value problems

Applications

To apply the integrating factor method, a linear equation must first be written in which form?

For y prime plus p of x y equals q of x, the integrating factor is which function?

Multiplying y prime plus p y by the integrating factor produces which left side?

In the general solution of a linear equation, the homogeneous term C e^(-integral p) is also called what?

The chapter has solved separable and linear first-order equations. An equation like y prime = x + y is which type?

For y prime + 2y = q, the integrating factor is e to the integral of 2 dx, which is e to which multiple of x? Answer like 2x.

For y prime + 2y = 3, the steady-state particular solution is 3/2. As a fraction, what is it? Answer like 3/2.

An RC circuit charges toward Q = C V. As a two-letter symbol, what is the steady charge? Answer like Q with a subscript described.

The equation y prime + p y = q y^n is called Bernoulli's equation, nonlinear for n not 0 or 1. Which substitution linearizes it?

The homogeneous transient decays at rate p. For p = 2, the transient halves in time ln 2 over 2. As a fraction, what is the half-life? Answer like ln 2/2.