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Unformatted text preview: Practice Problems 1 for MTH G131: Fall 2006 1). Find the general solution of the following ODE: dy dx = x 2 y (1 + x 3 ) 2). Find the solution of the following initial value problem, and determine the interval of existence: dx dt = 2 t 1 + 2 x , x (2) = 0 3). Newton’s law of cooling states that the surface temperature of an object changes at a rate proportional to the difference between the temperature of the object and that of its surroundings. Let u ( t ) be the object’s temperature at time t , and let u be the fixed temperature of the surroundings. Then du dt = k ( u- u ) where k is constant. a) Find the solution satisfying the initial condition u (0) = u . b) Suppose the temperature of a cup of tea is 200 F when freshly poured. One minute later it has cooled to 190 F in a room at 70 F. How long must elapse before the coffee reaches a temperature of 150 F ? 4). Find eigenvalues and eigenvectors of the matrix A = 3- 2 2- 2 5). Find the general solution of the ODE d dt x y = 2- 1 3- 2 x y 6).6)....
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- Fall '08
- Constant of integration, Boundary value problem, dt, Picard–Lindelöf theorem