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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+
Assume that (X, d) is a metric space and let (x1, : : : , x n ) be a nite set of pointsof X. Elustrate , using only the denition of open, that the set X\(x1, : : : , x n ) obtain
The order of a differential equation is the huge derivative there in the differential equation. Under the differential equations as listed above in equation (3) is a first order di
kolushushi borrowed tsh 250000/- and paid135000/- as interest in 3 years. what rate of interest was paid
Prove that the area of a rhombus on the hypotenuse of a right-angled triangle, with one of the angles as 60o, is equal to the sum of the areas of rhombuses with one of their angles
20! 18!
calculate the shortest distance between A and B 40degrees west and 50 degrees east respectively laying along 57 degrees north
how to do mathematical proofs
integral 0 to 4 integral 0 to y root of 9+ysquredxdy
What is a close figure in plane?
Arc Length and Surface Area Revisited We won't be working any instances in this part. This section is here exclusively for the aim of summarizing up all the arc length and su
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