Initial Condition
Definition
The starting value or values of a function or system at the beginning of a given scenario.
Analogy
Think of initial conditions as the ingredients you have when you start baking a cake. They determine what you have to work with before any changes or transformations occur.
Related terms
Differential Equation: An equation that relates an unknown function to its derivatives, often used to model change over time.
Boundary Condition: A condition that specifies the behavior of a function or system at the boundaries or limits of a given scenario.
Initial Value Problem: A type of differential equation problem that involves finding a solution based on both an initial condition and a differential equation.
"Initial Condition" appears in:
Study guides (1)
Practice Questions (14)
Find the particular solution to the differential equation y' = 2cos(x) with the initial condition y(0) = 3.
Given the differential equation y' = 4x - 6, find the solution that satisfies the initial condition y(2) = 5.
Given the differential equation y' = -2/x, find the particular solution that satisfies the initial condition y(1) = 2.
Find the solution to the differential equation y' = 1/(x^2) with the initial condition y(1) = 1.
Given the differential equation y' = 2e^(2x), find the solution that satisfies the initial condition y(0) = 2.
Given the differential equation y' = 2x - y, find the particular solution that satisfies the initial condition y(0) = 1.
Given the differential equation dy/dx = x^2 + y and the initial condition y(1) = 3, identify the initial x, initial y, and slope values for the first step of Euler's method.
Solve the differential equation: dy/dx = 4e^x, given the initial condition y(0) = 1.
Solve the differential equation: dy/dx = 2sin(x), given the initial condition y(0) = 0.
Solve the differential equation: dy/dx = 5x^4, given the initial condition y(1) = 10.
Solve the differential equation: dy/dx = 1/x^2, given the initial condition y(1) = 2.
The solution to the differential equation dy/dx = 5y with an initial condition y(0) = 2 is given by:
The solution to the differential equation dy/dx = 0.5y with an initial condition y(0) = 10 is given by:
The solution to the differential equation dy/dx = -0.5y with an initial condition y(0) = 8 is given by:
Are you a college student?
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
Resources
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.