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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 slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))
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What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
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report on shares and dovidend using newspaer
Find the second derivative of the below given equation Y= e x cosx
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The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equivalent the lesser. What is the value of the lesser integer? Let x =
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