Download KMU 237-21 HW-V

KMÜ 237-21 Engineering Mathematics
HOMEWORK 5 (Due January 11, 2017)
NAME:
NUMBER:
1. A hot pie that was cooked at a constant temperature of 150 C is taken directly from
an oven and placed outdoors in the shade to cool on a day when the air
temperature in the shade is 30 C. After 5 minutes in the shade the temperature of
the pie had been reduced to 90 C. Determine;
a) the temperature of the pie after 10 minutes and
b) the time required for the pie to reach 30 C.
2. Use Laplace transforms to solve the following system
for the unknown functions y(x) and z(x).
y¢ - y - 2z = 1
z¢ - 4y - 3z = -1
4.
3.
Solve the given differential equation
x dy + y dx = x3 y6 dx
y(0) = 1
z(0) = 2
5. Solve the following differential equation
y’’’’- y = 0
Solve the following differential equation
(x3 D3 + 3 x2 D2 – 2 x D + 2) y = 3 x4
7. Let u = u(x,y).
By integration find the solution to
ux = 2x
where
u(0,y)=y2,
6. Solve the given initial value problem
sinx dx + y dy = 0
y (0) = 1
8. Determine whether the given differential equation is exact or not and then solve the differential
equation by using the solution methods of exact differential equations
(t2 + x2) dt + (2 t x – x) dx = 0
9.
The differential equation
x2


d2y
dy
 x  x2  n2 y  0
2
dx
dx
where n is a parameter, is called
…………………………………………………….......................of order…....…
If n is zero the general solution of this equation is given by the following equation:
y  A J 0 ( x)  B Y0 ( x) where A and B are arbitrary constants.
J0 is called the …………………………………
Y0 is called the …………………………………