Practice Final

# Practice Final - After the rst year, the population is 27....

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Math 127 - S2008 Practice Test for the Final Examination 1. Show that the function y = C - cos( x ) x 2 is a solution of the diﬀerential equation x 2 y 0 + 2 xy = sin( x ) . For what value of C does the solution satisfy the initial condition y (2 π ) = 0? 2. Find the general solution to the diﬀerential equation y 0 = xy 4 e 3 x 2 . 3. Solve the initial value problem dX dt = sin( t ) s X 3 cos( t ) , X (0) = 4 . 4. A curve passes through the point (1,2) and has the property that at every point P on the curve, the slope of the curve is equal to three times the square of the slope of the straight line connecting P to the origin. Find the equation of the curve. 5. A population P ( t ) obeys the logistic equation. The initial value of the population is 20.
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Unformatted text preview: After the rst year, the population is 27. After a many years, the population seems to be converging to 10,000. Find the dierential equation that P ( t ) satises. 6. Find the general solution of the second order equation 2 y 00 + 10 y + 13 y = 0 . Then nd the solution satisfying y (0) = 10, y (0) = 0. 7. Find the MacLaurin Series of the function f ( x ) = sin( x 2 ) and the radius of convergence of that series. 8. Expand f ( x ) = x 2 (1+ x ) 3 as a MacLaurin Series. Use the expansion to help you determine the value of the innite sum X n =2 (2 n-1) 2 3 n . 1...
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## This note was uploaded on 09/26/2008 for the course MAT 127 taught by Professor Guan-yushi during the Fall '07 term at SUNY Stony Brook.

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