Presentation on theme: "Differential Equations"— Presentation transcript:
1Differential Equations By Johnny Grooms and Ryan BarrAP Calculus BCMrs. Miller, 2nd Period
2Basic Differential Equations When solving, the answer is an equationSolveThe answer is a general solution with a constantAnswer:If given a certain condition such as (1,2) then find a particular solution2 = 1+c and therefore c=1The answer would be
3Separable Differentiable Equations Rewrite so that y and dy are on the same side of the equation opposite x and dx.can be rewritten to beThen take the Integral of each side of the equationRemember to write + c on the x-side of the equation in order to account for the constant that is formed when taking an integral
4Separable Differentiable Equations Remember that after taking the integral of each side of the equation, you might end up with the equation where there is y= , substitute A in for this and then solve the equation using conditions given.Find the general solution and also a particular solution for (4,2)
5More on Differential Equations and Word Problems If y is directly proportional to x thenIf the rate of change of y is directly proportional to y thenThe general solution for this is
6More on Differential Equations and Word Problems Acceleration, Velocity, Speed, and DistanceNet Distance:Total Distance:a=dv/dtv=dS/dt
7Slope FieldsAt a point on the graph, draw short lines of the relative slope of the equation at the pointUsed to visualize the direction of the slope of the equationMay also be given a point in which to sketch a solution for on the slope field.