Try to find an integrating factor.blondie1234 said:1. Find all real solutions: (dx/dt)-2x=cos(3t)
2. Homework Equations
3. I really don't know where to start here. Any advice to get me on my feet would be appreciated.
A linear differential equation is an equation that involves a dependent variable and its derivatives, with the highest derivative being of the first degree. It can be written in the form of y' = F(x,y), where y is the dependent variable, x is the independent variable, and F is a function of x and y.
The general solution of a linear differential equation is a solution that contains all possible solutions to the equation. It is usually expressed in terms of one or more arbitrary constants, which can take on different values to represent different specific solutions.
To solve a linear differential equation, you can use a variety of methods such as separation of variables, integrating factors, or the method of undetermined coefficients. These methods involve manipulating the equation to isolate the dependent variable and solve for it.
The order of a linear differential equation is the highest derivative present in the equation. For example, a first-order linear differential equation would have a first derivative, while a second-order linear differential equation would have a second derivative.
Linear differential equations are commonly used in fields such as physics, engineering, and economics to model and predict various systems and processes. Examples include describing the growth of a population, the motion of a pendulum, and the flow of electricity in a circuit.