Working with differential equations and Newton's Law of Cooling.

At 4:30 PM on Monday, a Virginia criminalist was called to the scene of a homicide. She noted that the body temperature of the deceased was 85.5 deg. while the air temperature was 78 deg. Thirty minutes later, the deceased's body temperature was 82 deg. Assuming the air temperature stayed constant, what is the estimated time of death of the body? (Assume a normal body temperature of 98.6 deg)

Working with half lives.

The highly radioactive material Novarium has a half-life of 18.5 months. If our physics lab currently has 26 grams of Novarium, how many grams will be left in the lab two years from now?

differential equation

Please state the method used and show the work required to obtain the answer. solve the differential equation: 12y^"" + 46y^''' + 48y" - 11 y' -30y =0

Solution for an IVP differential equation problem

Using the method of undetermined coefficients, find the solution of the system: X'=AX + B that satisfies the initial condition: X(0)=( 0 1 -1). A and B are matrices defined in the attached Notepad file. Note: When solving the homogeneous soln, exhibit a fundamental matrix psi(t) and also the special fundamental matrix phi(t) satisfying phi(0)=I.

Differential Equations

Please see the attached file for the fully formatted problems. (i) Consider the differential equation: x. = x^2 , x(0) given x(0)>0 Find the solution of x(t) of this equation in terms of x(0) and show that there is a T, which depends on x(0), such that lim x(t) = infinity t --> T- (ii) Find the solution of the differential equation x.. - x = e^-t/2 , x(0) = 0, (0) = 1, Using the reduction of order method.