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What is Newston's first law of motion?
An object in motion tends to stay in motion. IE, law of inertia.

What is newtons second law of motion?
Force equals Mass times Acceleration.

What is Newtons Third law of motion?
For every action, there is an equal and opposite reaction.

What is the first law of thermodynamics?
The first law of thermodynamics states that energy is neither created nor destroyed, that is simply changes from one state to another.

What is the second law of thermodynamics?
in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state. Also referred to as entropy, which is the degree of disorder in a system.

List some properties of an exponential function.
 e^{0}=1
 e^{at+c}=e^{at}*e^{c}
 e^{at} is never zero
 If a > 0 then lim e^{at} = ∞ (t→∞) and lim e^{at} = 0 (t→−∞).
 If a < 0 then lim e^{at} = 0 (t→∞) and lim e^{at} = ∞ (t→−∞).

How do you determine the order of an ordinary differential equation?
The highest differential determines the order.

Describe how to use substitution to solve an Ordinary Differential Equation (ODE).
 If you have a solution, you can plug it in to the original ODE. For example: x'=3x. Check to see if x=e^{3t }is a solution. Simply plug and chug.
 x'=3e^{3t}, so 3e^{3t}=3e^{3t}.

What is the solution to the ODE x'=ax?
x(t)=Ce^{at}

What is the derivative of X^{c}?
Using the power rule, we have c*X^{c1}.

What is the derivative of of Sin(x)?
Cos(x) dx.

What is the derivative of cos(x)?
sin(x) dx

What is the derivative of tan(x)?
sec^{2}(x) dx

What is the integral of e^{x}?^{}
e^{x}dx.

What is the derivative of ln(x)?
1/x dx.

Using the product and quotient rule, what is the derivative of u*v?
v du + u dv

What is the derivative of kx, where k is constant?
k dx.

what is the answer to cos^{2}(Θ)+sin^{2}(Θ)?
cos^{2}(Θ)+sin^{2}(Θ)=1

What is the trigonometric identity involving sin(2Θ)?
sin(2Θ)=2*sin(Θ)*cos(Θ)

What is the integral of (ax+b)^{r} dx?
 ∫(ax+b)^{r} dx = (ax+b)^{r+1}
 a(r+1)

Explain separation of variables for solving DE's
Attempt to get all variables on separate sides of the equal sign. Then do the integration to get the solution.

