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Consider the equation
x2y′′+ xy′- y = 4x ln x
(a) Verify that x is a solution to the homogeneous equation.
(b) Use the method of reduction of order to derive the second solution to the homogeneous equation as Cx-1
(c) Use the method of variation of parameters to show that the general solution of the equation can be written as
y = x(ln x)2- x ln x + c1x + c2x-1
greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s
Mean, variance, skewness and kurtosis of a probability density function f(r)that has a distribution of a passive scalar filed in a stationary isotropic turbulence for initial condi
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1. What is the present value of a security that will pay $15,000 in 15 years if securities of equal risk pay 8.9% annually? Round your answer to the nearest cent. 475,858.20
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Simple derivatives Example Differentiate following. (5x 3 - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th
If the point (a,2a) is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus then a belongs to
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