Question

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

Answer #1

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!

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...

Solve the following differential equations through order
reduction.
(a) xy′y′′−3ln(x)((y′)2−1)=0.
(b) y′′−2ln(1−x)y′=x.

Solve the following 2nd Order differential equation and find
y(x):
y'' + 2y' +y = x + e-x
y(0) = 0, y'(0) = 0.

solve differential equation ((x)2 - xy +(y)2)dx - xydy
= 0
solve differential equation (x^2-xy+y^2)dx - xydy =
0

Solve the following differential equation using the power series
method. (1+x^2)y''-y'+y=0

Solve the following differential equation using taylor series
centered at x=0:
(2+x^2)y''-xy'+4y = 0

Solve the following equation by using the frobenius method
y ′′ + xy′ + (1 − 2 * x ^ (-2) )y = 0
No point is given.

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...

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

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