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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+
20 equations that equal 36
A circular disc of 6 cm radius is divided into three sectors with central angles 1200, 1500,900. What part of the circle is the sector with central angles 1200. Also give the ratio
Following are some examples of complex numbers. 3 + 5i √6 -10i (4/5) + 1 16i 113 The last t
Also, their inability to apply the algorithm for division becomes quite evident. The reason for these difficulties may be many. We have listed some of them below. 1) There are n
Question 1: (a) Show that, for all sets A, B and C, (i) (A ∩ B) c = A c ∩B c . (ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). (iii) A - (B ∪ C) = (A - B) ∩ (A - C).
Verify Liouville''''''''s formula for y "-y" - y'''''''' + y = 0 in (0, 1) ?
2
a-1/a =8 find
area of r=asin3x
A department store faces a decision for a seasonal product for which demand can be high, medium or low. The purchaser can order 1, 2 or 3 lots of this product before the season beg
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