Can it be done in a word file? Document Preview: Differentia

Can it be done in a word file? Document Preview: Differentia

Can it be done in a word file? Document Preview: Differential Equations Take-home Exam 1 Summer 2012 Due Monday, June 25 at 11:59 pm Name_____________________________________________ Directions: Show your work whenever possible for full/partial credit. Note that a correct answer is worth one point; the remaining points are for the supporting work. Once you have a complete solution to an equation, you may stop, even if the solution could be simplified further or made explicit. [1] (42 points) Solve each differential equation. (a) 4 4 2 2 2 2 = x y – x + y – dx dy .(b) xy e x dx dy x 4 ( + 1) – = (c) [2] (14 points) Solve the following initial-value problem: (3 2) ( 2 ) 0 2 x + y – dx + x + y dy = ; y(2) = 3 [3] (6 points) Show that is an implicit solution to the differential equation: !. [4] (6 points) Find values for ” for which #$is a solution to the differential equation: %% % &'() [5] (10 points) A tank contains 480 gallons of water in which 60 lbs of salt are dissolved. A saline solution containing 0.5 lbs of salt per gallon is pumped into the tank at the rate of 2 gallons per minute. The well-mixed solution is pumped out at the rate of 4 gallons per minute. Set up an initial value problem which can be solved for the amount A of salt in the tank at time t. [6] (6 points) Consider the following differential equation: y x dx dy x dxd y sin x ln 2 3 3 – + = (a) Is the equation linear or nonlinear? (b) Is it a partial or ordinary differential equation? (c) What is the order of the equation? [7] (10 points) Verify that y x ln x 2 = is a solution of %%% &%% % *+on the interval (0,) . [8] (6 points) Determine if the following differential equation is homogeneous or not. ( Attachments: TWT2012062277….pdf