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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+
Unit circle A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle. The unit circle is very useful in Trigonometry. (b) x 2 + ( y - 3) 2
Evaluate algebraic word problems: A utility has three nuclear facilities which supply a total of 600 megawatts (Mw) of electricity to a particular area. The largest facility
What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))
f(x)=sin x+cos x in the interval {0,90}
what is 10+5..
two Indiana state senate candidates must decide which city to visit the day before the november election. The same four cities are available for both candidates. These cities are l
If a triangular sail has a horizontal length of 30 ft and a vertical height of 83 ft , Determine the area of the sail? a. 1,245 ft 2 b. 1,155 ft 2 c. 201 ft 2 d. 2,4
Explain the Absorbing States of a markov chain.
Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
The sum of the squares of two consecutive positive odd integers is 74. What is the value of the smaller integer? Let x = the lesser odd integer and let x + 2 = the greater odd
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