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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+
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is
Right-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x>a without in fact letting x be a.
The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+
A non-empty set or group of which all the sets under concern are subsets is known as the universal set. In any part of application of set theory, all the sets under concern might l
1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s
Hydrostatic Pressure and Force - Applications of integrals In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on t
tracing of cardidods
samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
What is Linear Simultaneous Equations?
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