char808 said:So if s(1) = 10
s(1) = (15/4)(1)^4/3 + c
10 = 15/4 + c
c = 25/4
(just trying to clear up my understanding of these types of problems. thank you for the help.)
An initial value question is a type of mathematical problem that involves finding the value of a variable at a specific starting point, or initial value. This value is often denoted as "y0" and is used to find the solution to the equation or problem.
To solve an initial value question, you first need to identify the equation or problem and determine the initial value, if given. Then, you can use various mathematical methods such as substitution, integration, or differential equations to find the solution for the variable at the initial value.
Initial value questions are important because they allow us to understand the behavior of a variable over time or in a specific situation. They are often used in real-life scenarios to model and predict outcomes in fields such as physics, economics, and engineering.
The main difference between an initial value question and a boundary value question is the starting point. In an initial value question, the value at the starting point is given, while in a boundary value question, the values at the boundaries or endpoints are given. Additionally, boundary value questions often involve multiple solutions, while initial value questions typically have a single solution.
No, an initial value question typically has only one solution. This is because the initial value serves as a starting point and determines the behavior of the variable throughout the problem. However, there are some cases where an initial value question may have multiple solutions, such as in chaotic systems or in nonlinear equations.