Question

Get the general solution for, by an auxiliary equation
:

y'''' -y=0

Answer #1

Given the differential equation to the right y''-3y'+2y=0
a) State the auxiliary equation.
b) State the general solution.
c) Find the solution given the following initial conditions
y(0)=4 and y'(0)=5

Find the general solution to the differential equation: y’’ – 6
y’ + 13y = 0
Find the general solution to the differential equation: y’’ +
5y’ + 4y = x + cos(x)

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Given the third order homogeneous constant coefficient equation
y′′′+4y′′+y′−26y=0
1) the auxiliary equation is ar3+br2+cr+d= ? =0.
2) The roots of the auxiliary equation are ? (enter answers as a
comma separated list).
3) A fundamental set of solutions is (Enter the fundamental set
as a commas separated list y1,y2,y3)

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

Find the general solution of the equation
• y″+ y = cosx
i) The homogeneous solution yh(x) and yp(x)
ii) The general solution using the initial conditions y(0)=1 and
y'(0)=1

Find the general solution of the given differential
equation.
y'' + 12y' + 85y = 0
y(t) =

Find the general solution of the equation:
y" + 4y = t^2 + 3e^t
salisfying y(0) = 1 and y'(0) = 0

1. Find the general solution to the differential equation y''+
xy' + x^2 y = 0 using power series techniques

ﬁnd the general solution of the given differential equation
1. y''−2y'+2y=0
2. y''+6y'+13y=0
ﬁnd the solution of the given initial value problem
1. y''+4y=0, y(0) =0, y'(0) =1
2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2
use the method of reduction of order to ﬁnd a second solution of
the given differential equation.
1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1

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