Page 351 - Handbook Of Integral Equations

n
k
6 .For g(x) = cos(λx) A k x , a solution of the equation 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 can be found by the method of undetermined coefficients.
n
k
7 .For g(x) = sin(λx) A k x , a solution of the equation 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 can be found by the method of undetermined coefficients.

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

n
◦
10 .For g(x) = cos(λx) A k exp(µ k x), a solution of the equation 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 can be found by the method of undetermined coefficients.

n
◦
11 .For g(x) = sin(λx) A k exp(µ k x), a solution of the equation 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 can be found by the method of undetermined coefficients.

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 330