EXAM1 - Problem 1(10pts Solve the general first order...

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Unformatted text preview: Problem 1 (10pts) . Solve the general first order linear differential equation dy dt + p ( t ) y = g ( t ) , using the integrating factor technic. 1 Problem 2 (10pts) . Let α ∈ R be a real number. Solve dy dx = y α , y (0) = 1 . (Hint: Treat the case α = 1 separately.) 2 Problem 3 (10pts) . Solve ( 2 xe x 2 y- 1 y ) + ( e x 2 y + x y 2 ) dy dx = 0, y (0) = 2006. 3 Problem 4 (12pts) . Consider the 3 rd order linear differential equation ( ? ) y (3)- y 00- 2 y- 3 y = 0 . y (0) = 0 , y (0) = 1 , y 00 (0) = 2 . Find the 1 st order differential equation in R 3 equivalent to ( ? ). 4 Problem 5 (12pts) . Solve the general homogeneous 2 nd order linear differential equation with constant coefficients ay 00 + by + cy = 0 . Analyze all the three cases possible, i.e., b 2- 4 ac > 0, b 2- 4 ac < 0, and b 2- 4 ac = 0. 5 Problem 6 (10pts) . Solve the nonhomogeneous 2 nd order linear equation y 00 + y- 2 y = 2 t, y (0) = 0 , y (0) = 1 ....
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EXAM1 - Problem 1(10pts Solve the general first order...

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