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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+
What is the annual interest rate on an account in which earns $948 in simple interest over 36 months along with an initial deposit of $7,900? Using the easy interest formula In
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Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution) 140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with
Frequently, tests that yield abnormal results are repeated for confirmation. What is the probability that for a usual person a test will be at least 1.5 times as high as the upper
Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
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Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?
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solve x+y= 7 and x-y =21
Explain Bachet Equation?
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