- #1
Feodalherren
- 605
- 6
Homework Statement
Homework Equations
DifEqs
The Attempt at a Solution
y ' = 4C1e-4xSinX - 4C2e-4xCosX
y'(0) = -1
-1 = 0 - 4C2
Therefore
C2 = 1/4
Not correct. What am I doing wrong?
Feodalherren said:What am I doing wrong?
An IVP, or initial value problem, is a type of mathematical problem that involves finding a function that satisfies a given differential equation and initial conditions. It is commonly used in physics, engineering, and other scientific fields.
Finding the constants for a given IVP allows us to determine the specific solution to the problem and make accurate predictions about the behavior of the system being modeled. It also helps us to better understand the underlying principles and relationships involved.
The process of finding the constants for a given IVP involves solving the differential equation using various mathematical techniques, such as separation of variables or integration. The initial conditions are then used to determine the values of the constants in the solution.
When solving a given IVP, it is often assumed that the system being modeled is continuous and differentiable, and that the initial conditions are well-defined and within the applicable domain of the solution. Additionally, certain physical or mathematical constraints may also be assumed based on the specific problem at hand.
Sure, let's say we have the differential equation dy/dx = 2x + 1 and the initial condition y(0) = 3. By solving the equation and plugging in the initial condition, we can find that the solution is y = x^2 + x + 3. In this case, the constant term is 3, which is determined by the initial condition.