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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+
the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?
advanteges of duality
Before independence, Bangladesh was called Ceylon East Pakistan Bhutan Bangalore Which of the following countries does not have a monarch as head of state? Canada Australia Eire
how to divide fractions
Determine the value of the unknown side of a right triangle: The two legs of a right triangle are 5 ft and 12 ft. How long is the hypotenuse? Now Let the hypotenuse be c ft.
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
what is quantity ?
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
Q. Addition Involving Negative Numbers? Ans. When you add together positive and negative numbers, there are essentially three possibilities that you can encounter. Let's e
-255=-14t-t
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