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1. Solve the given differential equation, subject to the initial conditions:
. x2y''-3xy'+4y = 0
. y(1) = 5, y'(1) = 3
2. Find two linearly independent power series solutions for each differential equation about the ordinary point x=0
Y'' - xy' - (x+2)y=o
3. Use the definition of the Laplace Transform, to find
L{e-t cosht}
4. Find f(t) if : f(t)=L-1
5. Solve : y'+y= f(t)
where: f(t) = { 1 if 0 ≤ t < 1
{-1 if t ≥ 1
Recall that if f(t) = { g(t) if 0 ≤ t < a
{ h(t) if t ≥ 1
Then f(t)=g(t)-g(t)u(t-a)+h(t)u(t-a)
6. y'(t) = cos t+
(x^2+x+3)^4
ABC is a right angled triangle in which ∠A = 900. Find the area of the shaded region if AB = 6 cm, BC=10cm & I is the centre of the Incircle of ?ABC. Ans: ∠A =90 0 BC
a. Write an exponential function that could model the information in this graph. b. Describe a business, scientific (not mathematical), or economic situation for what thi
Q. Example of negative number? If you take an elevator 8 stories down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories up .
Give the example of Exponents? When a number is multiplied several times, it is easier to write it as an exponent. For example, four multiplied to itself three times, is writte
Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2
What is Permutations explain with examples? Each arrangement of a set of elements is called a permutation. In other words, every possible way (order) of writing a group of lett
1/2+3/4
Definition of a Function Now we need to move into the second topic of this chapter. Before we do that however we must look a quick definition taken care of.
do you have 3 digit and 4 digit number problem
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