21 (k, l) = (2µ/2)*µl z2 (k, l) = (-2µ'/2)*el.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Explain the determine blue Or slove the Q
![Example F
The Lagrange method applied to the equation
2(k + 2, e) = 42(k, l + 1)
(5.113)
gives X2 = 4µ or A1
211/2 and A2 = -2µ1/2. Therefore, special solutions
are
(k,e) = (2u/2)*u
(5.114)
and
2(k, l) = (-2µ'/2)*µ°.
(5.115)
Multiplying these two equations by C1(u) and C2(u) and summing over u
gives the general solution
z(k, l) = 2*[f(k + 2l) + (–1)*g(k + 20)],
(5.116)
where f and g are arbitrary functions of k + 2l.
Likewise, the separation-of-variables method, žp(k, l) = ChDe, gives the
equations
De+1 = a?,
Ck+2
4Ck
(5.117)
De
where we have written the "separation constant" in the form a?. The solutions
to equations (5.117) allow us to determine zp(k, l); it is
k+2l
Zp(ki, l) = [A1a*+24 + A2(-)*a*+2412*,
(5.118)
where A1 and A2 are arbitrary constants. Summing over a gives the general
solution expressed by equation (5.116).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ae7d80b-7c46-4638-8712-b4be41e1370a%2Fc795e8a3-3d4d-468a-b765-aefc5c96b9a8%2Fvxpqwl8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example F
The Lagrange method applied to the equation
2(k + 2, e) = 42(k, l + 1)
(5.113)
gives X2 = 4µ or A1
211/2 and A2 = -2µ1/2. Therefore, special solutions
are
(k,e) = (2u/2)*u
(5.114)
and
2(k, l) = (-2µ'/2)*µ°.
(5.115)
Multiplying these two equations by C1(u) and C2(u) and summing over u
gives the general solution
z(k, l) = 2*[f(k + 2l) + (–1)*g(k + 20)],
(5.116)
where f and g are arbitrary functions of k + 2l.
Likewise, the separation-of-variables method, žp(k, l) = ChDe, gives the
equations
De+1 = a?,
Ck+2
4Ck
(5.117)
De
where we have written the "separation constant" in the form a?. The solutions
to equations (5.117) allow us to determine zp(k, l); it is
k+2l
Zp(ki, l) = [A1a*+24 + A2(-)*a*+2412*,
(5.118)
where A1 and A2 are arbitrary constants. Summing over a gives the general
solution expressed by equation (5.116).
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