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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+
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
Inverse Functions : In the last instance from the previous section we looked at the two functions f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that ( f o g ) ( x )
An $80.00 coat is marked down 20%. It does not sell, so the shop owner marks it down an additional 15%. What is the new price of the coat? Find out 20 percent of the original p
[2 5] . [7 8}
The distance from the sun to the earth is approximately 9.3 × 10 7 miles. What is this distance expressed in standard notation? In order to convert this number to standard not
how to solve the problems? methods to solve the question of joint lines
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
Level Curves or Contour Curves Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are t
Maximize P=3x+2y Subject to x+y =6 x =3 x =0,y =0
A card is drawn from a well shuffled deck of cards (i) What are the odds in favour of getting spade? (Ans: 1:3, 3:1, 3:10, 1:25) (ii) What are the odds against getting a spa
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