Page 267 - Handbook Of Integral Equations

8 .For g(x)= e µx n A k cos(λ k x), the solution 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 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.

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 246