Page 439 - Handbook Of Integral Equations

k
2 . For a polynomial right-hand side, g(x)= n A k x , the equation has a solution of the
◦
k=0
form
n
k
y(x)= B k x ,
k=0
where the constants B k can be found by the method of undetermined coefficients.
k
3 .For g(x)= e λx n A k x , the equation has a solution of the form
◦
k=0
n
k
y(x)= e λx B k x ,
k=0
where the constants B k can be found by the method of undetermined coefficients.

4 .For g(x)= n A k cos(λ k x), the equation has a solution of the form
◦
k=1
n n

y(x)= B k cos(λ k x)+ 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.

◦
5 .For g(x)= n A k sin(λ k x), the equation has a solution of the form
k=1
n n

y(x)= B k cos(λ k x)+ 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.

k
6 .For g(x) = cos(λx) n A k x , the equation has a solution of 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.

k
◦
7 .For g(x) = sin(λx) n A k x , the equation has a solution of 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), the equation has a solution of 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.

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 419