Separable differential equations

The  exercise appears under the Differential equations Math Mission. This exercise shows how to separate the y's from the x's on two different sides of the equation.

Types of Problems
There are six types of problems in this exercise:
 * 1) Which of the following is the solution to the differential equation: The student is asked to find the solution to the differential equation using the initial condition.Separable differential equations(1).png
 * 2) Determine $$a$$ and $$b$$: The student is asked to determine the value(s) of a and b using the two equations and initial condition.
 * 3) Determine $$t$$: The student is asked to determine the value(s) of $$t$$ using the derivative and properties given.
 * 4) Determine the value of $$y$$: The student is asked to determine the value of $$y$$ given the value of $$x$$ and the graph of the differential equation.
 * 5) Determine the value of $$x$$: The student is asked to determine the value of $$x$$ using the initial value and differential equation.
 * 6) Which of the differential equations below are separable: The student is to determine which differential equations are separable by using factoring.

Strategies
Knowledge of derivatives, implicit differentiation, differential equations, and factoring are encouraged to ensure success on this exercise.