quiz_08ode_runge4th(1) - Multiple-Choice Test Chapter 08.04...

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08.04.1 Multiple-Choice Test Chapter 08.04 Runge-Kutta 4th Order Method 1. To solve the ordinary differential equation ( ) 5 0 , sin 3 2 = = + y x xy dx dy , by Runge-Kutta 4 th 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 Runge-Kutta 4 th order method is most nearly (A) –0.25011 40 10 × (B) –4297.4 (C) –1261.5 (D) 0.88498 3. Given ( ) 5 3 . 0 , 3 2 = = + y e y dx dy x , and using a step size of 3 . 0 = h , the best estimate of ( ) 9 . 0 dx dy Runge-Kutta 4 th order method is most nearly (A) -1.6604 (B) -1.1785 (C) -0.45831 (D) 2.7270
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