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quiz_08ode_runge2nd(1) - Multiple-Choice Test Chapter 08.03...

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08.03.1 Multiple-Choice Test Chapter 08.03 Runge-Kutta 2nd Order Method 1. To solve the ordinary differential equation ( ) 5 0 , sin 3 2 = = + y x xy dx dy by the Runge-Kutta 2 nd order method, you need to rewrite the equation as (A) ( ) 5 0 , sin 2 = = y xy x dx dy (B) ( ) ( ) 5 0 , sin 3 1 2 = = y xy x dx dy (C) ( ) 5 0 , 3 cos 3 1 3 = = y xy x dx dy (D) ( ) 5 0 , sin 3 1 = = y x dx dy 2. Given ( ) 5 3 . 0 , sin 5 3 2 = = + y x y dx dy and using a step size of 3 . 0 = h , the value of ( ) 9 . 0 y using the Runge-Kutta 2 nd order Heun method is most nearly 3. Given ( ) 5 3 . 0 , 5 3 1 . 0 = = + y e y dx dy x and using a step size of 3 . 0 = h , the best estimate of ( ) 9 . 0 dx dy using the Runge-Kutta 2 nd order midpoint method most nearly is
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08.03.2 Chapter 08.03 08.03.2 4. The velocity (m/s) of a body is given as a function of time (seconds) by ( ) ( ) 0 , 1 ln 200 + = t t t t v Using the Runge-Kutta 2 nd order Ralston method with a step size of 5 seconds, the distance in meters traveled by the body from 2 = t to 12 = t seconds is estimated
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