Question

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))

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

($4.2 Reduction of Order):
(a) Let y1(x) = x be a solution of the homogeneous ODE xy′′
−(x+2)y′ + ((x+2)/x)y = 0. Use the reduction
of order to find a second solution y2(x), and write the general
solution.

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...

Verify that the given function is a solution and use Reduction
of Order to find a second linearly independent solution.
a. x2y′′ −2xy′ −4y = 0, y1(x) = x4.
b. xy′′ − y′ + 4x3y = 0, y1(x) =
sin(x2).

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

The indicated functions are known linearly independent solutions
of the associated homogeneous differential equation on (0, ∞). Find
the general solution of the given nonhomogeneous equation.
x2y'' + xy' + y = sec(ln(x))
y1 = cos(ln(x)), y2 = sin(ln(x))

Use the METHOD of REDUCTION OF ORDER to find the general
solution of the differential equation y"-4y=2 given that y1=e^-2x
is a solution for the associated differential equation. When
solving, use y=y1u and w=u'.

Solve the 2nd Order
Differential Equation using METHOD OF REDUCTION
Please don't skip
steps!
(x-1)y"-xy'+y=0 x>1
y1(x)=x
My professor is
getting y2(x)=e^x and I don't understand how!

Use the method of reduction of order to find the
general solution of the following differential equation. (t^2)
d^2y/dt^2 + t dy/dt + (t^2-1/4) y = 0, y1(t) = sin t/sqrt(t)

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