Question

1. If x1(t) and x2(t) are solutions to the differential equation x" + bx' + cx...

1. If x1(t) and x2(t) are solutions to the differential equation

x" + bx' + cx = 0

is x = x1 + x2 + c for a constant c always a solution? Is the function y= t(x1) a solution?

Show the works

2. Write sown a homogeneous second-order linear differential equation where the system displays a decaying oscillation.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If x1(t) and x2(t) are solutions to the differential equation x"+bx'+cx = 0 1. Is x=...
If x1(t) and x2(t) are solutions to the differential equation x"+bx'+cx = 0 1. Is x= x1+x2+c for a constant c always a solution? (I think No, except for the case of c=0) 2. Is tx1 a solution? (t is a constant) I have to show all works of the whole process, please help me!
Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note that this is not...
Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note that this is not a constant coefficient differential equation, but it is linear. The theory of linear differential equations states that the dimension of the space of all homogeneous solutions equals the order of the differential equation, so that a fundamental solution set for this equation should have two linearly fundamental solutions. • Assume that y = x^r is a solution. Find the resulting characteristic equation for r....
Write down a homogeneous second-order linear differential equation with constant coefficients whose solutions are: a. e^-xcos(x)...
Write down a homogeneous second-order linear differential equation with constant coefficients whose solutions are: a. e^-xcos(x) , e^-xsin(x) b. x , e^x
The following are solutions to homogeneous linear differential equations. Obtain the corresponding differential equation with real,...
The following are solutions to homogeneous linear differential equations. Obtain the corresponding differential equation with real, constant cocfficients that is satisfied by the given function: a) y=4e^2x+3e^-x b) y=x^2-5sin3x c) y=-2x+1/2e^4x d) y=xe^-xsin2x+3e^-xcos2x
a) The homogeneous and particular solutions of the differential equation ay'' + by' + cy =...
a) The homogeneous and particular solutions of the differential equation ay'' + by' + cy = f(x) are, respectively, C1exp(x)+C2exp(-x) and 3x^3. Give the complete solution y(x) of the differential equation. b) If the force f(x) in the equation given in a) is instead f(x) = f1(x) + f2(x) + f3(x), where f1(x), f2(x), and f3(x) are generic forces, what would be the particular solution? c) The homogeneous solution of a forced oscillator is cos(t) + sin(t), what is the...
The indicated function y1(x) is a solution of the associated homogeneous differential equation. Use the method...
The indicated function y1(x) is a solution of the associated homogeneous differential equation. Use the method of reduction of order to find a second solution y2(x) and a particular solution of the given nonhomoegeneous equation. y'' − y'  = e^x y1 = e^x
1250) y=Aexp(Bx)+Fexp(Gx) is the particular solution of the second order linear differential equation: (y'') + (...
1250) y=Aexp(Bx)+Fexp(Gx) is the particular solution of the second order linear differential equation: (y'') + ( 2y') + (-24y) = 0, subject to the boundary conditions: y=4, and y'=1 when x=0. Find A,B,F, and G, where B>G.
Second-Order Linear Non-homogeneous with Constant Coefficients: Find the general solution to the following differential equation, using...
Second-Order Linear Non-homogeneous with Constant Coefficients: Find the general solution to the following differential equation, using the Method of Undetermined Coefficients. y''− 2y' + y = 4x + xe^x
Consider the two vector-functions listed below. Justify your answers for each question. x1(t) = [t, 2t]...
Consider the two vector-functions listed below. Justify your answers for each question. x1(t) = [t, 2t] and x2(t) = [t , t^2] (a) Are the vector-functions x1(t) and x2(t) linearly independent on the interval (−∞,∞)? (b) Does there exist a point t0 such that the constant vectors x1(t0) and x2(t0) are linearly dependent? (c) Can the vector-functions x1(t) and x2(t) be solutions to a first-order homogeneous linear system? DIFF. EQUATIONS
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + (...
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + ( -4y') + ( 3y) = ( 2) + ( -7)x. Find A,B,F,G, where A>B.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT