Hello and thank you for posting your question to brainmass!

The solution is attached below in two files. The solution is the same in both files , only the format is different.
On is in Acrobat pdf format and the other is in MS Word format, so you can choose your favorite application.

However ...

Solution Summary

A differential equation is solved. The solution is detailed and well presented.

... you should notice that the two differential equations we need ... Now, both of your equations are second-order ... 2 as the highest order of the differentials (that is ...

... Fourier transform applied to Dirac delta distribution yields "1". The equation (11) becomes a simple ordinary differential equation of 1'st order: (17) whose ...

... Question 10: (1 points) Make the change of variable for the homogenous differential equation. and find , where. ... This is a separable differential equation. ...

Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2. ...

Solving differential equations.. ... 1. Find both the first and second order differentials (y' and ... integrating factor to convert the following equation into "exact ...

1). Given the differential equation for 1. L[y]= y''+2by'+b2y = exp(-bx)/x2, x>0 ; a) Find the complementary solution of (1) by solving L[y] = 0. b) Solve (1 ...