Baumer8993 said:Homework Statement
y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x
Homework Equations
Differential Equations.
The Attempt at a Solution
I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I am not sure.
A differential equation is a mathematical equation that relates the values of a function to its derivatives. It is commonly used to model processes that involve rates of change, such as the growth of populations or the flow of electricity.
A solution set is a collection of all possible solutions to a given differential equation. These solutions can be in the form of a function or a set of values that satisfy the equation.
To construct a differential equation from a solution set, you need to identify the independent and dependent variables, as well as the derivatives involved. Then, you can use the basic rules of differentiation to create an equation that relates the variables and their derivatives.
Some common methods for constructing differential equations from solution sets include separation of variables, substitution, and finding the general solution using integration. These methods involve manipulating the given solution set to create an equation that satisfies the given conditions.
Constructing a differential equation from a solution set is important because it allows us to model and understand real-world phenomena. These equations can help us make predictions and solve problems related to rates of change, making them a valuable tool in many scientific fields.