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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+
Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is ( f o g ) ( x ) = f ( g ( x )) In other
If ABCD isaa square of side 6 cm find area of shaded region
Question: Solve the initial value problem 2x'' +x'-x =27 Cos2t +6 Sin 2t, x(0)=2 , x'(0)= -2 by using Laplace transform method.
In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
poa is a straight line in circle,wher o is center of circle,b is any pointjoined with p.prove that pa>pb
Find the full fourier Series of e^x on (-l,l)in its real and complex forms. (hint:it is convenient to find the complex form first)
Consider the system of linear equations X + ay = 1 2x + 8y = b Where a and b are real numbers. (a) Write out the augmented matrix for this system of linear equations.
what is (x-y)(x+y)
Example of Product moment correlation The given data was acquired during a social survey conducted in a described urban area regarding the yearly income of described families
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