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Die Heuning Pot Literature Guide
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Introduction to Differential Equations - At A Glance:

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 = 5x2 + 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) = x3 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 = x2 + 4x is a solution to the IVP

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