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**Unformatted text preview: **2 dt x e) dx x 2 f) 7 1 dx x x g) ( 29 x x dx + h) ( 1) x dx + i) 3 2 (2 5 1) x x x dx-+ + j) 1 x dx x + 3 Differential equation : an equation involves x , y and derivatives of y . Particular solution of differential equation: 4 Example 2 : Find the general solution of 2 1 '( ) f x x = , x and find the particular solution that satisfies the initial condition (1) f = . Example 3 : Solve the differential equation a) ( 29 ( 29 '( ) 2 3 2 3 , (3) f x x x f =-+ = b) 2 "( ) , '(0) 6, (0) 3 f x x f f = = = 5 Example 4 : A ball is thrown upward with an initial velocity of 64 ft/s from an initial height of 80 feet. a. Find the position function giving the height s as a function of the time t . b. When does the ball hit the ground? 6...

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