Question
Asked Oct 22, 2019
In Exercises 1-6 use variation of parameters to find a particular solution.
y9y tan 3x
1.
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In Exercises 1-6 use variation of parameters to find a particular solution. y9y tan 3x 1.

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Step 1

Result used:

General form of ODE
P(x)y'+Q(x)y R(x)
Complementary function for distinct real roots:
mx
m,x
Variation of param eters method
W(yi, y)=
PI Ax)(x)+B (x)y (x) where
y>R(x)
dx and B (x)
R(x)
W(x.y)
A (x)=
W(x. y)
General solution:
y(x)CF+PI
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General form of ODE P(x)y'+Q(x)y R(x) Complementary function for distinct real roots: mx m,x Variation of param eters method W(yi, y)= PI Ax)(x)+B (x)y (x) where y>R(x) dx and B (x) R(x) W(x.y) A (x)= W(x. y) General solution: y(x)CF+PI

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Step 2

The given differential equation is

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Step 3

Find the complementary function as follows.

The auxiliary ...

cos 3x
sin3x
W(y, y2)=
3 sin 3x
3cos 3x
cos 3x(3cos 3x) sin 3x(3 sin 3x)
3(cos 3x+ sin23x)
=3
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cos 3x sin3x W(y, y2)= 3 sin 3x 3cos 3x cos 3x(3cos 3x) sin 3x(3 sin 3x) 3(cos 3x+ sin23x) =3

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