Question

Formulate a system of linear 1st-order ODEs from the higher order ODEs below.

y^(4) + 2y''' + 3y'' 4y' + 5y = f(t)

Answer #1

.

take

.

so the first-order system is

.

Solve the system of linear equations. If the system has an
infinite number of solutions, set w = t and solve for x, y, and z
in terms of t.)
x + y + z + w = 6
2x+3y - w=6
-3x +4y +z + 2w= -1
x + 2y - z + w = 0
x, y, z, w=?

Solve the second-order linear differential equation
y′′ − 2y′ − 3y = −32e−x using the method of variation of
parameters.

find the general solution.
1- y^6(4)+12y''+36y=0
2-6y^(4)+5y'''+7y''+5y'+y=0
3-y^(4)-4y'''+7y''-6y'+2y=0

(Higher Order DE) Find the general solution of y'''− 2y''− y'+
2y = e^x?

Solve the linear system by Gaussian elimination. 2x+2y+2z= 0
–2x+5y+2z= 1 8x+ y+4z=–1

solve for y:
1. dy/dx= xe^y separable
2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear

solve the linear order y' - 2y = cos(3x). solve for y.

Consider the linear first order system [16]
x′ = x + y (1) y′ =4x−2y. (2)
(a) Determine the equilibria of System (1)-(2) as well as their
stability. [6]
(b) Compute the general solution of System (1)-(2). [6]
(c) Determine the solution of the initial value problem
associated with System (1)-(2), with initial condition x(0) = 1,
y(0) = 2.

Decide whether or not the following equations are linear:
(a) d^2/dx^2y(x) = -8(y(x))^2 is a
- linear equation
- non-linear equation
(b) d/dx(yx) + sin(4y) = 0 is a
- linear equation
- non-linear equation
(c) sin(8x)*d/dxy(x) + y(x) = 7x is a
- linear equation
- non-linear equation
(d) d/dtx(t) +3x = -8t^3 is a
- linear equation
- non-linear equation
(e) sin(5y(x))d/dxy(x) + y(x) = 9x is a
- linear equation
- non-linear equation

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

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 27 minutes ago

asked 31 minutes ago

asked 36 minutes ago

asked 50 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago