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For the differential equation: (2-x^2)y′′ - xy′ + x^2y = 0
(a) Compute the recursion formula for the coefficients of the power series solution centered at x0 = 0 and use it to compute the first three nonzero terms of the solution with y(0) = 0, y′(0) = -36.
(b) Show that the solution given in (a) is an odd function (Hint: what is an when n is even?)
Write a paper on the causes and effects of water pollution in Lake Huron. The paper will be provided to the state's fish and game board as well as various committees for improving public health.
Does the function f(n) = 10 - n from the set of integers to the set of integers have an inverse? If so, what is it?
Susan Duke borrowed $20,000 for four years to purchase a car. The simple interest loan has a rate of 8.2% per year. What is the maturity value of the loan?
A linear transformation L:V->V is said to be idempotent if L dot L = L. If L is idempotent, show that there exists a basis S={a1,a2,...,an} for V such that L(ai)=ai for i= 1,2,...,r
Develop a short procedure for either (a) a mass letter mail-out or (b) the creation of an expense report. Ensure your procedures:
When using the substitution method, how can you tell if a system of linear equations has no solution?
A voltage V across a resistance R generates a current I=V*R. If a constant voltage of 14 volts is put across a resistance that is increasing at a rate of 0.7 ohms per second when the resistance is 3 ohms, at what rate is the current changing?
SAVINGS ACCOUNTS If Jackson deposits $100 at the end of each month in a savings account earning interest at the rate of 8%/year compounded monthly.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
base elevation of 8700 ft, mountain peak in colorado rises 14407 ft over distance of 15844 ft. find the grade of the peak.
Find the x-coodinate of the local maximum of f(x) = x3 - 2.3x2 - 2.8x. Find the x-coodinate of the local maximum of f(x) = x3 - 2.1x2 -1.7x.
If a hospital patient is given 100 milligrams of medicine which leaves the bloodstream at 14% per hour, how many milligrams of medicine will remain in the system after 10 hours? Use the function A(t) = Iert.
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