# Thread: Forst order linear ordiny differential equation

1. ## Forst order linear ordiny differential equation

Hei!

Can anyone help me to give an excatly explanation/translation of the following differential equations:
1. T'(t)=-k .(T_(t)-T_(r)) where T_r is a constant

2. y"_(t)=-10

Thanx

2. ## Re: Forst order linear ordiny differential equation

Originally Posted by Haytham1111
Hei!

Can anyone help me to give an excatly explanation/translation of the following differential equations:
1. T'(t)=-k .(T_(t)-T_(r)) where T_r is a constant

2. y"_(t)=-10

Thanx
#1 looks like the DE for Newton's Law of Cooling ...

$\dfrac{dT}{dt} = -k(T - T_r)$, where $T_r$ is the ambient temperature surrounding an object that has temperature $T$ as a function of time.

The rate of change of temperature of an object is directly proportional to the difference between the object's temperature and its surroundings.

#2 looks like the approximation of acceleration due to gravity near the Earth's surface ...

$a = \dfrac{dv}{dt} = \dfrac{d^2y}{dt^2} = -10 \, m/s^2$

The rate of change of an object's velocity in free-fall (in the absence of air resistance) is a constant.