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.
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