Question

Differential Equations problem

If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

Answer #1

If
y1= e^-3x is a solution of the differential equation y "'+ y" - 4y'
+ 6y = 0. What is the general solution of the differential
equation?

Oridinary Differential equations:
given that y=sinx is a solution of
y(4)+2y'''+11y''+2y'+10y=0,
find the general solution of the DE.

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....

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

1) find a solution for a given differential equation
y1'=3y1-4y2+20cost ->y1 is not y*1 & y2 is not y*2
y2'=y1-2y2
y1(0)=0,y2(0)=8
2)by setting y1=(theta) and y2=y1', convert the following 2nd
order differential equation into a first order system of
differential equations(y'=Ay+g)
(theta)''+4(theta)'+10(theta)=0

differential equations
find the solution to the initial value problem
y’’ + y(x^2) = 0
y(0) = 0
y’(0) = 0

The indicated function y1(x) is a solution of the
given differential equation. Use reduction of order or formula (5)
in Section 4.2,
y2 = y1(x)
e−∫P(x) dx
y
2
1
(x)
dx (5) as instructed, to find a
second solution y2(x).
y'' + 36y = 0; y1 =
cos(6x)
y2 =
2) The indicated function y1(x) is a solution of the
given differential equation. Use reduction of order or formula (5)
in Section 4.2,
y2 = y1(x)
e−∫P(x) dx
y
2
1...

Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Find the fundamental solution to the following differential
equation.
y''+y'-2y=0, t0=0

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 6 minutes ago

asked 11 minutes ago

asked 18 minutes ago

asked 26 minutes ago

asked 27 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago