First Order Linear Differential Equations (FOLDE)

What is the process to determine if an explicit linear equation is a solution to a FOLDE?

1. Find appropriate derivatives of given equation
2. Plug into differential equation to determine if the given equation is a solution

What is the process to determine if an implicit linear equation is a solution to a FOLDE?

1. Take the derivative with respect to x of both sides of the given equation
2. Solve for dy/dx

Be sure to match the given differential equation
Look back to x to see if a simplification is possible

What is the process to determine if an explicit linear equation is a solution to the initial value condition and the FOLDE?

1. Plug in the initial value and solve
2. Solve according to #1

What are the two ways to solve for FOLDE?

1. Separation of variables
2. Integrating factor

What is is the process to solve for a FOLDE by separation of variables?

1. Separate dy/dx into the left and right side of the equation
2. Integrate
3. Solve for y
4. Plug-in initial value if given for specific solution

What is the process to solve for a FOLDE by integrating factor?

What are the three types of FOLDEs?

If the solution to a FOLDE is implicit, then how can the data be graphed?

Level curves such that g(x,y) = c

What are practical uses of FOLDEs?

Model bacterial growth, half-life decay

What does a growth FOLDE look like?

Where y(x) = y0e^(cx)

What does a decay FOLDE look like?

y(x) = y0e^(-cx)