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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+
Q. There are 10 students on the school debating team. How many different ways can the team choose a president and a secretary? Ans. There are 10 choices for the president
Find out if the following set of vectors are linearly independent or linearly dependent. If they are linearly dependent get the relationship among them. Solution : Ther
Which of the subsequent terms does NOT describe the number 9? Nine is NOT prime since it has 3 factors; 1, 3, and 9. Prime numbers have only 2 factors.
An irrigation system uses a straight 30m sprinkler pipe which is capped at one end and arranged so that all water is released directly downwards and pivots around a central point.
how do you divide
4 1/2 ----2----1/3=3
y 2 = t 2 - 3 is the actual implicit solution to y'= t/y, y(2) = -1. At such point I will ask that you trust me that it is actually a solution to the differential equation. You w
Factor following. x 2 - 20 x + 100 Solution In this case we've got three terms & it's a quadratic polynomial. Notice down as well that the constant
use the distributive law to write each multiplication in a different way. the find the answer. 12x14 16x13 14x18 9x108 12x136 20x147
We have to enclose a field along with a fence. We contain 500 feet of fencing material & a building is on one side of the field & thus won't require any fencing. Find out the dime
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