# 1_2 - Solutions 1.2-Page 17 Problem 5 Find a function y = f...

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Solutions 1.2-Page 17 Problem 5 Find a function satisfying the given differential equation and the prescribed initial condition. ) ( x f y = 2 1 + = x dx dy ; 1 ) 2 ( = y Integrating both sides of the differential equations yields: + + = + = C x dx x x y 2 / 1 ) 2 ( 2 2 1 ) ( Now, the initial condition is used to find C . 5 1 4 1 4 2 1 2 2 2 ) 2 ( = = + = + = + + = C C C C y Therefore, 5 2 2 ) ( + = x x y

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Problem 9 Find a function satisfying the given differential equation and the prescribed initial condition. ) ( x f y = 2 1 1 x dx dy = ; 0 ) 0 ( = y The integration of the differential equation is done according to the inside cover of the textbook. Integrating both sides yields: + = = C x dx x x y 1 2 sin 1 1 ) ( The initial condition is used to find C. 0 0 ) 0 ( sin ) 0 ( 1 = = + = C C y x x y 1 sin ) ( =
Problem 16 Find the position function of a moving particle with the given acceleration , initial position , and the initial velocity ) ( t x ) ( t a ) 0 ( 0 x x = ) 0 ( 0 v v = . 4 1 ) ( + = t t a , v , 1 0 = 1 0 = x Integrating both sides of the acceleration equation to get an equation for velocity yields: () + + = + = C t dt t t v 2 / 1 4 2 4 1 ) ( The initial velocity is used to solve for C. 5

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1_2 - Solutions 1.2-Page 17 Problem 5 Find a function y = f...

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