Question

The indicated function y_{1}(x) is a solution of the
given differential equation. Use reduction of order, to find a
second solution dx **Please do not solve this via the
formula--please use the REDUCTION METHOD ONLY.

y_{2}(x)= ??

Given: y'' + 2y' + y = 0; y_{1} =
xe^{−x}

Answer #1

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...

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'' + 64y = 0; y1 =
cos(8x)
y2 =

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))/y12(x)dx (5)
as instructed, to find a second solution
y2(x).4x2y'' + y = 0; y1 = x1/2 ln(x)
y2 = ?

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).
x2y'' -11xy' + 36y = 0; y1 = x6
y2 =

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'' + 100y = 0;
y1 = cos 10x
I've gotten to the point all the way to where y2 = u y1, but my
integral is wrong for some reason
This was my answer
y2= c1((sin(20x)+20x)cos10x)/40 + c2(cos(10x))

The indicated function y1(x) is a solution of the associated
homogeneous differential equation. Use the method of reduction of
order to find a second solution y2(x) and a particular solution of
the given nonhomoegeneous equation.
y'' − y' = e^x
y1 = e^x

let
y1=e^x be a solution of the DE 2y''-5y'+3y=0 use the reduction of
order method to find a second linearly independent solution y2 of
the given DE

Consider the differential equation x2y''+xy'-y=0,
x>0.
a. Verify that y(x)=x is a solution.
b. Find a second linearly independent solution using the method
of reduction of order. [Please use y2(x) =
v(x)y1(x)]

the indicated function y1(x) is a solution of the associated
homogeneous equation.use reduction of order formula.
1. (1-x^2)y''+2xy'=0; y1=1
2. 16y''-24y'+9y=0; y1= e^3x/4

Follow the steps below to use the method of reduction of order
to find a second solution y2 given the following
differential equation and y1, which solves the given
homogeneous equation:
xy" + y' = 0; y1 = ln(x)
Step #1: Let y2 = uy1, for u = u(x), and
find y'2 and y"2.
Step #2: Plug y'2 and y"2 into the
differential equation and simplify.
Step #3: Use w = u' to transform your previous answer into a
linear...

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