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Contents
11
17
Dierential Equations
17.1
17.2
17.3
17.4
17.5
17.6
17.7
First Order Dierential Equations . . . .
First Order Homogeneous Linear Equations
First Order Linear Equations . . . . . . .
Appr
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224
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Chapter 4. Higher Order Linear Equations
If Eq. (9) is to hold for all t in I, then it must certainly be true at any three distin
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222
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Chapter 4. Higher Order Linear Equations
Since Eq. (2) involves the nth derivative of y with respect to t, it will, so to speak,
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4.1 General Theory of nth Order Linear Equations
223
y0 , y0 , . . . , y(n1)
so that Eqs. (6) do not have a solution. Therefore a nec
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CHAPTER
4
Higher Order Linear
Equations
The theoretical structure and methods of solution developed in the preceding chapter
for seco
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Chapter 3. Second Order Linear Equations
Then, substituting for u2 (t) in Eq. (9) and simplifying, we obtain
u1 (t) =
3 csc t s
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3.6
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Variation of Parameters
189
As in Example 1, we now set the terms involving u1 (t) and u2 (t) in Eq. (20) equal to
zero; that is
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Chapter 3. Second Order Linear Equations
then a particular solution of Eq. (16) is
! t
! t
y2 (s)g(s)
y1 (s)g(s)
ds + y2 (t)
ds,
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Variation of Parameters
187
a quotient (rather than a sum or a product) of sin t or cos t. Therefore, we need a different
approa
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Chapter 3. Second Order Linear Equations
35. In this problem we indicate an alternative procedure7 for solving the differential
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