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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 satised 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 coecients: 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 nd a second solution of the dierential 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 so that the solution to the initial value problem y 00 + 3 y4 y = 0 ,y (0) = ,y (0) = 1 , converges to 0 as t + ....
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This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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