# Solving Linear Homogeneous Differential Equations

Not what you're looking for?

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

##### Purchase this Solution

##### 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.

##### 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 ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.