At a Glance - Initial Value Problems
An Initial Value Problem (IVP) is a differential equation combined with one or more initial conditions. An initial condition gives some extra information about the solution. In order to be a solution to an IVP, a function has to satisfy both the differential equation and all initial conditions.
This will allow to find the value of that pesky constant we're always adding onto our solutions, so that we can get a unique solution.
Example 1
Is the function y = 4x + 1 a solution to the IVP |
Example 2
Find a solution to the IVP |
Example 3
Determine if the function y = 5x^{2} + 3x satisfies the IVP y" = 10 and y(0) = 3. |
Exercise 1
Determine if the function y = 4e^{ -x} is a solution to the IVP
y" + y ' = 0 and y(0) = 4.
Exercise 2
Determine if the function f (x) = x^{3} is a solution to the IVP
3f (x) = xf '(x) and f (0) = 2.
Exercise 3
Determine if the function y = x + 2 is a solution to the IVP
Exercise 4
Determine if the function f (x) = sin x is a solution to the IVP
f ^{(3)}(x) = -f '(x) and f (0) = 0.
Exercise 5
Determine if the function y = x^{2} + 4x is a solution to the IVP