Explore BrainMass

Solving Linear Homogeneous Differential Equations

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Consider the differential equation y''-2y'+2y = cost

(a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.

(b) Use Laplace Transforms to solve this differential equation with the initial conditions
y(0) = 1, y'(0) = 0

https://brainmass.com/math/calculus-and-analysis/solving-linear-homogeneous-differential-equations-129376

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Consider the differential equation y''-2y'+2y = cost

(a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.

Notice that the associated homogenous equation is linear second order with constant coefficients.

First, we "guess" a homogenous solution in the form:

Plugging this back into the equation we obtain:

The roots of the last equation are:

So the solution is:

As expected, we get two ...

Solution Summary

Solving Linear Homogeneous Differential Equations is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

\$2.49