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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+
Given f (x) =10x^3 - x^5 , find all intervals(in Interval Notation) of Concavity and the x-values of all Inflection Points.
P OLYNOMIALS : It is not once nor twice but times without number that the same ideas make their appearance in the world. 1. Find the value for K for which
a man can row a bangka at a rate of 5 km/h in still water. It takes 10 minutes longer to row upstream a distance of 2km than he takes to row downstream. What is the rate of the cur
difference between PERT and CPM
2+2=
Now we need to discuss graphing an equation. The first question which we have to ask is what accurately is a graph of an equation? A graph is the set of all the ordered pairs whos
When there are 4 dots how many chords are they
Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp
Find an integrating factor for the linear differential equation and hence Önd its general solution: SOLVE T^ 2 DY DX+T2
The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $35, what price tag will he put on the item? To ?nd out the price he s
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