Particular solution for non-homog second order linear diff-eq

I have already found the first part of the general solution for the equation below, but am not sure how to find the particular solution for the e^(-4x) part of the equation. Please find the particular solution for e^(-4x) in this problem and show all details.thanks. d²y/dx² + 6dy/dx + 9y = e^(-4x)

Particular solution for non-homog second order linear diff-eq

I have already found the first part of the general solution for the equation below, but am not sure how to find the particular solution for the 7e^x part of the equation. Please find the particular solution for 7e^x in this problem and show all details. d²y/dx² + 5dy/dx - 6y = 7e^x

Orthogonal trajectories

Find the equation for the family of curves orthogonal to the one-parameter family y=e^cx where c is rewritten first with c isolated on one side of the equation Do i use algebra to isolate the c and how do i go about doing that, then do i integrate?

A corpse's temperature is specified at two hours interval. Given the room temperature, to determine the time of murder.

A corpse was found at exactly 2:00 p.m. The detective measures the temperature of the body and it is 35 degrees C. He measures it again two hours later and it's 30 degrees C. If the room temperature is 20 degrees C then at what time did the murder occur (assuming that the normal body temp of a living person is 37 degrees C)?

Interest

A person's fortune increases at a rate to the square of they're present wealth. If the person had one million dollars a year ago and has two million today then how much will the person be worth in six months?

Polonium

Polonium-210 has a half life of 140 days If a sample has a mass of 200 mg find a function describing the mass that remains after t days When will the mass be reduced to 10 mg?

Tank

In a tank containing 100 gallons of fresh water, 10 lbs of salt was added instead of 20 lbs. To correct the mistake, fresh water was added at the rate of 3 gallons per minute while draining off the well stirred salt solution from the tank at the same rate. How long will it take until the tank contains the correct amount of salt?

Differential Equations

(See attached file for full problem description) 1) The slope field for the system dx/dt = 2x + 6y dy/dt = 2x - 2y is shown to the right a) determine the type of the equilibrium point at the origin. b) calculate all straight-line solution. 2) show that a matrix of the form A =(a b; -b a) with b!=0 must have complex eig ...continues

Differential Equations Help

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Differential Equations Homework #02

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