Some sixth order homogeneous linear differential equation with constant coefficients has the following characteristic equation: (r^2-4r+4)(r^2-r-6)(r^2+6r+13)=0. What is the general solution of that sixth order differential equation? Your answer: y(x) = c1e^2x + c2xe^2x + c3x^2e^2x + c4e^-3x + c5e^3xcos(2x) + c6e^3xsin(2x) y(x) = c1e^-2x + c2e^2x + c3xe^2x + c4e^3x + c5e^3xcos(2x) + c6e^3xsin(2x) y(x) = c1e^2x + c2xe^2x + c3x^2e^2x + c4e^-3x + c5e^-3xcos(2x) + c6e^-3xsin(2x) y(x) = c1e^-2x + c2e^2x + c3xe^2x + c4e^3x + c5e^-3xcos(2x) + c6e^-3xsin(2x) None of the above
Added by Sandra W.
Close
Step 1
We want to find the values of x and y at which the characteristic equation will have the smallest possible value. To do this, we need to solve the equation _4r+4?_r-6)(r? + 6r+ 13)=0. To solve this equation, we'll use the quadratic formula. To do this, we'll Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 69 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In this question, you will solve the following non-homogeneous second-order differential equation with constant coefficients: d^2/dx^2 y(x) - (d/dx y(x)) - 12 y(x) = 2x + 6 (a) First find the solution y_H(x) to the homogeneous equation. Note: You must use capital A and capital B as your constants of integration. y_H(x) = (b) Next find a particular solution y_P(x) to the non-homogeneous equation. Try a solution of the form: y_P(x) = Cx + F. Enter your solution for y_P(x) = (c) Finally, enter the general solution y(x) =
Adi S.
Consider the second-order differential equation: y'' - 9y' + 14y = 3x^2 - 5 sin 2x + 7xe^{3x} Determine the form of the particular solution needed to use the method of undetermined coefficients for the nonhomogeneous equation (You do not need to solve the ODE!)
Find the general solution to a third-order linear homogeneous differential equation for y(x) with real numbers as coefficients if two solutions are known to be e^-2x and sin 3x. Determine the general solution y'' + y = 6e^x. y'' + 4y' + 4y = 5xe^-2x. Solve y' - 5y = 3e^x - 2x + 1. Solve y'' - 2y' + y = e^x / x.
Ekaveera K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD