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.