## Transcribed Text

Fundamentals of Mathematical Methods and Mechanics
Question 1
5 pts
A differential equation is given by,
#==
with the initial condition y(0)=1.
Find the value of y when x=1.70. Give your answer to 4 decimal places.
Question 2
5 pts
A differential equation is given by,
= xc
with the initial condition y(1)=2. =
Find the value of y when x=1.57. Give your answer to 4 decimal places.
Question 3
5 pts
By the method of substitution, evaluate the definite integral,
t I
when a = 9.0, b = 18.7 with t > 1. Give your answer to 3 decimal places.
Question 4
5 pts
By using implicit differentiation, find the gradient, dy/dx of the tangent to the curve,
x² + 4.0y³ - 4.5xy = 8.
at the point (2.4,2.29), giving your answer to 3 decimal places. Assume that this point satisfy the given equation of the
curve.
Question 5
5 pts
Consider the differential equation,
x-+2y=x2
with the initial condition y(1)=1.
Find the value of y when x=3.31. Give your answer to 4 decimal places.
Question 6
5 pts
Consider the differential equation,
dy
with the initial condition y(0)=3.
Calculate the value of y when x=23.6. Give your answer to 3 decimal places.
Question 7
5 pts
Consider the differential equation,
dy da = y + et sin x
with the initial condition y(0)=1.
From the particular solution, find the value of y when x=0.80 radian. Give your answer to 4 decimal places.
Question 8
5 pts
For the following equation,
log(y) - log(y+5.94)+ log10.58 = 2log(x) =
Determine the value of y when x = 1.40, giving your answer to 4 decimal places.
Question 9
5 pts
For the following equation,
log(6.2-y)-log(y)= log(4.3+x4) - - 5log(x)
Determine the value of y when x= 2.1, giving your answer to 3 decimal places.
Question 10
5 pts
Two complex numbers are given by:
W =5+4i
z=7+3i =
Calculate the imaginery part of w/z. Give your answer to 3 decimal places.
Question 11
5 pts
A 2nd-order differential equation is given by,
a dx² y + b +
The complementary function is.
=
For a=1.39, b=1.53 and c=3.11, find the value of p to 4 decimal places.
Question 12
5 pts
A 2nd-order differential equation is given by,
+ b +
The complementary function is.
yc=e°X(Csin(qx) + Dcos(qx))
For a=1.33,b=0.15 and c=3.88, find the value of q to 3 decimal places.
Question 13
5 pts
A non-homogeneous 2nd-order differential equation is given by,
a
dx² d2y + b dx + =
The particular integral is,
Yp=pe2x
Assume no special cases in this problem.
For a=0.22, b=8.8 and c=-3.94, find the value of p to 3 decimal places.
Question 14
5 pts
A non-homogeneous 2nd-order differential equation is given by,
a d2y 2 + b dx =
The particular integral is,
yp=px+q
Assume no special cases in this problem.
For a=0.57, b=10.9 and c=-3.57, find the value of q to 4 decimal places.
Question 15
5 pts
Avector p is given by,
p = 7.01i + 6.69j + 3.63k
Find the magnitude of pto 4 decimal places.
Question 16
5 pts
Two vectors p and q are given by,
p = 3.08i + 1.92j + 4.01k
q = 2.81i + 2.23j + 1.19k
From the vector cross product pxq. determine the coefficient of the j unit vector to 4 decimal places.
Question 17
5 pts
Two vectors p and q are given by,
p=4.3i+-4.7j
q=2i+4j =
Calculate the cosine of the angle between vector p and vector q to 3 decimal places.
Question 18
5 pts
Two vectors p and q are given by,
p = - -3.96i + 2.66j
q = 3.469i + 1.284j
Find the dot product p.q to 4 decimal places.
Question 19
5 pts
A 2nd-order differential equation is given by,
a dx² + =
The complementary function is,
YC=AeP*+Beax
where p>q. For a=2.86,b=10.6 andc=-2.90,findthe value of a to 4 decimal places.
Question 20
5 pts
A 2nd-order differential equation is given by,
The complementary function is,
where p> a. For a=0.52, b=9.5 and c=-7.05, find the value of p to 3 decimal places.

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Question No Answer

1 -3.8046

2 6.0417

3 37.317...