Solving Differential Equations 5.1

Power Reducing Formulas: Integrating With Trig Identities Recall:

Solving Differential Equations Finding a function when we know the derivative Solve by integration This is a general solution to the diff eq To find a particular curve we would need a point on the curve. This type of problem is called an Initial Condition or Initial Value Problem

Example Find the curve whose slope at any point Is x 3 and passes through the point (-2, 10). This is a general solution to the diff eq Particula r Solution

Example Velocity of an object is given by v(t)=9.8t +7 and s(0) = 23. Find the position of the object at t = 3. Velocity is the derivative of position s(0) = 23

Example Bubba is delivering a package of Godiva chocolates to his true love in a hot air balloon, which is rising at the rate of 12 ft/sec. When he reaches a height of 80 ft, he drops the package. How long until the package reaches the arms of his beloved valentine? Gravity is the only thing affecting the package! V(0) = 12 S(0) = 80 Quadrati c Formula