Examen Differential Equations

Differential equations

Oefententamen

Formulas to be used:


( )
dP P (t ) K K −P0
=k∗P ( t )∗ 1− ⇒ P ( t )= with A=
dt K 1+ A∗e
−kt P0

Assignment 1

You microwaved a warm bowl of soup. After removing the bowl from the microwave, it has a
temperature of 80 degrees Celsius. Let the bowl cool for 15 minutes and then measure the
temperature again. The temperature of the bowl after fifteen minutes is 67 degrees Celsius. The
temperature of the outside environment is 21 degrees Celsius. The differential equation of the
dT
cooling process is is =k (T omgeving −T ). T is in degrees Celsius and t is in minutes
dt

1. Show that
ln ( 4659 ) t is a solution to this differential equation.
T ( t )=59 e 15
+21
2. Calculate how long it takes till the temperature drops to 37 degrees Celsius.

, Assignment 2

In the pictures on the right you see a
directional field with the differential equation
. y ' ( x )=−xy+ x

1. On the worksheet, draw a solution
with the condition y ( 0 )=4 .
2. Solve the differential equation with
the condition y ( 0 )=0.
3. Calculate y (1) using Euler's method.
The initial condition is . y ( 0 )=0 Take
as step-sized Δ h=0,5 .