Introduction to differential equations and initial value problems

The  exercise appears under the Differential equations Math Mission. This exercise shows the basics of differential equations.

Types of Problems
There are six types of problems in this exercise:
 * 1) Find the sum of the two values: The student is asked to find the two values such that the first solution is a solution of the differential equation.
 * 2) Use substitution to match each differential equation on the left with an appropriate solution on the right: The student is asked to to match the differential equation with its solution.
 * 3) Which of the following is a general solution to the differential equation: The student is asked to determine the general solution to the differential equation than determine what C is for the particular solution with the initial condition.
 * 4) For what values of $$m$$ and  $$b$$  is $$y=mx+b$$  a solution: The student is asked to determine the values of $$m$$ and $$b$$ using the differential equation.Introduction to differential equations and initial value problems(2).png
 * 5) Which of the following equations is the general solution to the differential equation: The student is asked to determine the general solution to the differential equation.
 * 6) Answer the following questions for the differential equation given the initial condition: The student is asked to determine the first and second derivative of the differential equation at the initial condition and use this information to determine the behavior of the graph.

Strategies
Knowledge of derivatives, implicit differentiation, and differential equations are encouraged to ensure success on this exercise.
 * 1) Since $$y=mx+b$$, then the derivative of $$y$$ is equal is $$m$$
 * 2) When determining the end behavior of the graph, Implicit differentiation properties can be used.