Particular solution for nonhomogenous second order linear differential equation : d²y/dx² - y = xe^x

Please find the particular solution for xe^x in this problem and show all details. d²y/dx² - y = xe^x

Particular solution for non-homogeneous second order linear differential equation : d²y/dx² + 6dy/dx + 9y = e^(-4x)

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 a non-homogeneous second order linear differential equation : d²y/dx² + 5dy/dx - 6y = 7e^x

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.

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.

Interest and applications of derivatives.

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?

Concentration, Rate of Flow and Dilution

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?

Ordinary Differential Equation : Initial Value Problem : y''+2y'2y=sinat y(0)=y'(0)=0

Please see the attached file for the fully formatted problem. keywords : ODE IVP

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

Breking an Eigenvalue Equation into Domains and using Traces and Nodes

Examine the eigenvalue equation below and then break the domain into four different regions (like a>0) and b=0 is one such domain. Describe the behavior of the equation in each domain.... Please see the attached file for the fully formatted problems. keywords: differential equations, trace, node