Question

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

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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
Question 4 a) Solve y```` -4y```-5y``+36Y`− 36?=0 knowing that xe^2x it's a solution b) Determine the...
Question 4 a) Solve y```` -4y```-5y``+36Y`− 36?=0 knowing that xe^2x it's a solution b) Determine the general solution for a linear homogeneous differential equation in y(x) de fourth order, with real coefficients, knowing that a solution is given by x^3e^4x. Leave the calculations recorded in the activity
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...
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
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.
B. a non-homogeneous differential equation, a complementary solution, and a particular solution are given. Find a...
B. a non-homogeneous differential equation, a complementary solution, and a particular solution are given. Find a solution satisfying the given initial conditions. y''-2y'-3y=6 y(0)=3 y'(0) = 11 yc= C1e-x+C2e3x yp = -2 C. a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions y'''+2y''-y'-2y=0, y(0) =1, y'(0) = 2, y''(0) = 0 y1=ex, y2=e-x,, y3= e-2x
) Check that each of the following functions solves the corresponding differential equation, by computing both...
) Check that each of the following functions solves the corresponding differential equation, by computing both the left-hand side and right-hand side of the differential equation. (a) y = cos2 (x) solves dy/dx = −2 sin(x) √y (b) y = 4x + 1/x solves x dy dx + 2/x = y (c) y = e x 2+3 solves dy/dx = 2xy (d) y = ln(1 + x 2 ) solves e y dy dx = 2x
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....
Non homogeneous eq w constant; undetermined coefficients Find the general solution: 1) y" + 4y' +...
Non homogeneous eq w constant; undetermined coefficients Find the general solution: 1) y" + 4y' + 4y = xe^−x. 2) y" + 2y' + 5y = e^2x cos x. Determine a suitable form for a particular solution z = z(x) of the given equations 1) y" + 2y' = 2x + x^2e^−3x + sin 2x. 2) y" − 5y' + 6y = 2e^2x cos x − 3xe^3x + 5. 3) y" + 5y' + 6y = 2e^2x cos x −...
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0,...
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, ∞). Find the general solution of the given nonhomogeneous equation. x2y'' + xy' + y = sec(ln(x)) y1 = cos(ln(x)), y2 = sin(ln(x))
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT