This question is concerned with finding the solutions of the second order simultaneous equations
where a = 38, b = 9, c = 378, d = 79

(i) 

Find the particular solutions to the differential equations which satisfy the initial conditions x = 10 and y = 7 at t = 0 together with the condition
at t = 0..
For this part of the question give x as a function of t.
Omit the "x = " (8 marks)



Your Answer: 
77(cos(4t))+ 67(cos(5t)) 
Comment: 
The particular solution required in this part is x = ""


(ii) 

What is y as a function of t.
Omit the "y = " (8 marks)



Your Answer: 
462(cos(4t))+ 469(cos(5t)) 
Comment:  The particular solution required in this part is y = ""


(iii) 

What is the value of x at t = 0.56?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only ie. Omit the "x = " (2 marks) 


Your Answer: 
15.36105271 
Comment:  x = 15.36105271


(iv) 

What is the value of y at t = 0.56?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only ie. Omit the "y = " (2 marks) 


Your Answer: 
155.2952131 
Comment:  y = 155.2952131

