Question

Consider the following second order linear homogeneous ODE ?′′(?) − ??′(?) − ???(?) = ?, ?(?)...

Consider the following second order linear homogeneous ODE

?′′(?) − ??′(?) − ???(?) = ?, ?(?) = ?, ?′(?) = ??

  1. Solve the equation using the characteristic equation

  2. Transform the equation into a system (by setting ?1(?) = ?, ?2(?) = ?′ ) and solve it again

  3. State the nature of the critical point ?0, plot he portrait and say if ?0 is stable, stable and attractive or unstable (justify your answers)

  4. Solve the equation using Laplace transform

  5. Compare the three solutions and give your comments about the methods

*****typed answer preferred *******

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
find a basis of solutions for the 12th order homogeneous linear ODE with the following characteristic...
find a basis of solutions for the 12th order homogeneous linear ODE with the following characteristic equation: x^2(x+6)(x-1)^3(x^2-10x+41)(x^2+9)^2=0
y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a non-homogeneous linear second-order...
y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a non-homogeneous linear second-order differential equation withnon-constantcoefficients andnotof Euler type. (a) Write the Laplace transform of the Initial Value Problem above. (b) Find a closed formula for the Laplace transformL(y(t)). (c) Find the unique solutiony(t) to the Initial Value Problem
5.1 Application of Linear Second Order ODE): Consider the ‘spring-mass system’ represented by an ODE x′′...
5.1 Application of Linear Second Order ODE): Consider the ‘spring-mass system’ represented by an ODE x′′ (t) + 16x(t) = 5 sin 4t with ICs: x(0) = 2, x′ (0) = 1. Answer the questions (a)–(c): (a) Is there damping in the system? Why or why not? (b) Is there resonance in the system? Why or why not? (c) Solve the ODE.
3. Consider a second order linear homogeneous equation Ay'' + By' + Cy = 0 Suppose...
3. Consider a second order linear homogeneous equation Ay'' + By' + Cy = 0 Suppose that e^at, e^bt and e^ct are solutions (where a, b, c are constants). A. Show that e^at + e^bt + e^ct is also a solution. B. Show that two of the numbers among a, b, c are equal.
Q.3 (Applications of Linear Second Order ODE): Consider the ‘equation of motion’ given by ODE d2x...
Q.3 (Applications of Linear Second Order ODE): Consider the ‘equation of motion’ given by ODE d2x + ω2x = F0 cos(γt) dt2 where F0 and ω ̸= γ are constants. Without worrying about those constants, answer the questions (a)–(b). (a) Show that the general solution of the given ODE is [2 pts] x(t) := xc + xp = c1 cos(ωt) + c2 sin(ωt) + (F0 / ω2 − γ2) cos(γt). (b) Find the values of c1 and c2 if the...
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find...
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find two linearly independent solutions to the given equation. (b) Explain why your work in (a) only results in one linearly independent solution, y1(t). (c) Verify by direct substitution that y2=te^(3t) is a solution to y''−6y'+9y=0. Explain why this function is linearly independent from y1 found in (a). (d) State the general solution to the given equation
You can use dsolve in MATLAB...run simplify(...) on the solution...You should plot the homogeneous and the...
You can use dsolve in MATLAB...run simplify(...) on the solution...You should plot the homogeneous and the inhomogeneous solutions on the same graph, using the "plot" function of MATLAB. set the arbitrary constants to 1 Consider the homogeneous equation y'' + 3y' + 2y = 0. a) Solve it and set the c's to 1. Graph this transient solution using large dots in MATLAB. b) Now add on the right-hand side the linear term 12x. Solve the inhomogeneous equation y'' +...
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
Follow the steps below to use the method of reduction of order to find a second...
Follow the steps below to use the method of reduction of order to find a second solution y2 given the following differential equation and y1, which solves the given homogeneous equation: xy" + y' = 0; y1 = ln(x) Step #1: Let y2 = uy1, for u = u(x), and find y'2 and y"2. Step #2: Plug y'2 and y"2 into the differential equation and simplify. Step #3: Use w = u' to transform your previous answer into a linear...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT