Presentation on theme: "Differential Equations"— Presentation transcript:
1 Differential Equations By Johnny Grooms and Ryan BarrAP Calculus BCMrs. Miller, 2nd Period
2 Basic 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
3 Separable 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
4 Separable 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)
5 More 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
6 More on Differential Equations and Word Problems Acceleration, Velocity, Speed, and DistanceNet Distance:Total Distance:a=dv/dtv=dS/dt
7 Slope 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.