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Unformatted text preview: same rate. Let Q ( t ) be the amount of salt in the tank. Formulate and state an initial value problem satisﬁed by Q modeling this process. Make sure you write down both an equation and an initial condition that Q ( t ) must satisfy. 5. (15 points) Find the solution of the following initial value problem using the method of undetermined coeﬃcients: y 004 y + 3 y = t 2 + te 3 t , y (0) = 1 , y (0) = 0 . 6. (10 points) Use the method of reduction of order to ﬁnd a second solution of the diﬀerential equation: t 2 y 00 + 2 ty6 y = 0 , t > , knowing that y 1 ( t ) = t 2 is a solution. What is the general solution of the above equation? 7. (10 points) Find α so that the solution to the initial value problem y 00 + 3 y4 y = 0 ,y (0) = α,y (0) = 1 , converges to 0 as t → + ∞ ....
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, Boundary value problem

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