Page 263 - Handbook Of Integral Equations

k
6 .For g(x) = cos(λx) n A k x , the solution has the form
◦
k=0
n n
k k
y(x) = cos(λx) B k x + sin(λx) C k x ,
k=0 k=0
where the constants B k and C k are found by the method of undetermined coefficients.
k
7 .For g(x) = sin(λx) n A k x , the solution has the form
◦
k=0
n n
k k
y(x) = cos(λx) B k x + sin(λx) C k x ,
k=0 k=0
where the constants B k and C k are found by the method of undetermined coefficients.

◦
8 .For g(x)= e µx n A k cos(λ k x), the solution has the form
k=1
n n
y(x)= e µx B k cos(λ k x)+ e µx C k sin(λ k x),
k=1 k=1
where the constants B k and C k are found by the method of undetermined coefficients.

◦
9 .For g(x)= e µx n A k sin(λ k x), the solution has the form
k=1
n n
y(x)= e µx B k cos(λ k x)+ e µx C k sin(λ k x),
k=1 k=1
where the constants B k and C k are found by the method of undetermined coefficients.
◦
10 .For g(x) = cos(λx) n A k exp(µ k x), the solution has the form
k=1
n n

y(x) = cos(λx) B k exp(µ k x) + sin(λx) B k exp(µ k x),
k=1 k=1
where the constants B k and C k are found by the method of undetermined coefficients.

11 .For g(x) = sin(λx) n A k exp(µ k x), the solution has the form
◦
k=1
n n

y(x) = cos(λx) B k exp(µ k x) + sin(λx) B k exp(µ k x),
k=1 k=1
where the constants B k and C k are found by the method of undetermined coefficients.

b
39. f(t)y(x + βt) dt = Ax + B.
a
Solution:
y(x)= px + q,
where
A B AI 1 β b b
p = , q = – 2 , I 0 = f(t) dt, I 1 = tf(t) dt.
I 0 I 0 I a a
0

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 242