Question

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.

Answer #1

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.

1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of
the second order linear differential equation:
(y'') + ( -9y') + ( 20y) = ( -9) + ( -8)x. Find A,B,F,G, where
A>B. This exercise may show "+ (-#)" which should be enterered into
the calculator as "-#", and not "+-#". ans:4

1249) The solution of some second order linear DEQ is
exp(-1x)[5sin(3x)+ 2cos(3x)] which can also be expressed as
A*exp(-D*x)*sin(F*x+G). Determine A,D,F, and G (degrees). ans:4
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + ( -8y') + ( -9y) = ( -8) + ( 3)x. Find A,B,F,G, where A>B. This exercise may show "+ (-#)" which should be enterered into the calculator as "-#", and not "+-#". ans:4

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

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

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.

Find the particular solution of the differential equation: y "+ 2y
'+ y = 3x + 5 + 4e^-x

For the below ordinary differential equation with initial
conditions, state the order and determine if the equation is linear
or nonlinear. Then find the solution of the ordinary differential
equation, and apply the initial conditions. Verify your
solution.
y''-3y'+2y=0; y(0)=1,y' (0)=2.

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

Consider the differential equation: .
Let y = f(x) be the particular solution to the differential
equation with initial condition, f(0) = -1.
Part (a) Find . Show or explain your work, do not
just give an answer.

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