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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+
Sequences and Series In this section we will be taking a look at sequences and infinite series. In fact, this section will deal approximately exclusively with series. Though
Describe the Properties of Inequalities ? Postulate In comparing two quantities, say a and b, there are exactly three possibilities. (1) a is less than b. (a b)
1. What is the value of Φ(0)? 2. Φ is the pdf for N(0, 1); calculate the value of Φ(1.5). 3. Suppose X ~ N(0, 1). Which, if either, is more likely: .3 ≤ X ≤ .4, or .7 ≤ X ≤
Question: Constrcut the adjacency matrix and the adjacency lists for the graph G below, where the weights associated with edges represent distances between nodes. If no edge is pre
2cos^2x-sinx=1......Find x
2/3=y-1/2
Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.
Q. Graphs of Sin x and Cos x ? Ans. The sine and cosine functions are related to the path that an object might take around a circle. Suppose a dolphin was swimming over
Data entry is performed in 2-person teams. Each 2-person team can enter 520 surveys per day. A selection of 7540 surveys must be entered by day''s end. How many total employees, wo
10 puzzles
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