Q1. To solve the ordinary differential equation

,

by Runge-Kutta 4^th order method, you need to rewrite the equation as

Q2. Given  and using a step size of , the value of  using Runge-Kutta 4^th order method is most nearly

- 0.25011

-4297.4

-1261.5
0.88498
Note: At the end of this document, see formulas used to answer this question as there are a few different versions of the Runge-Kutta 4^th order method.

Q3. Given , and using a step size of , the best estimate of  

Runge-Kutta 4th order method is most nearly

-1.6604
-1.1785
-0.45831
2.7270

Note: At the end of this document, see formulas used to answer this question as there are a few different versions of the Runge-Kutta 4^th order method.

Q4. The velocity (m/s) of a parachutist is given as a function of time (seconds) by

Using Runge-Kutta 4^th order method with a step size of 5 seconds, the distance traveled by the body from  to  seconds is estimated most nearly as

341.43 m      

428.97 m

429.05 m

 
703.50 m

Note: At the end of this document, see formulas used to answer this question as there are a few different versions of the Runge-Kutta 4^th order method.

Q5.  Runge-Kutta method can be derived from using first three terms of Taylor series of writing the value of , that is the value of at ,  in terms of  and all the derivatives of at .  If , the explicit expression for if the first five terms of the Taylor series are chosen for the ordinary differential equation

,

would be

Q6. A hot solid cylinder is immersed in an cool oil bath as part of a quenching process. This process makes the temperature of the cylinder,, and the bath, , change with time.  If the initial temperature of the bar and the oil bath is given as 600° C and 27°C, respectively, and

Length of cylinder = 30 cm

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