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The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...

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
(x)

dx        (5) as instructed, to find a second solution y2(x).

(1 − x2)y'' + 2xy' = 0;    y1 = 1

y2 =

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