Hi
Linear nonhomogeneous differential equations are solved using the following two techniques in the book: (1) Undetermined Coefficients (superposition and annihilator approaches), (2) Variation of Parameters.
The book says undetermined coefficients approaches do not apply when the forcing function (e.g. g(x) in this equation ay'' + by' + cy = g(x)) is: In(x), 1/x, tan(x), arcsin(x) and so on. And in such cases variation of parameters technique is used.
Q1: Does this mean variation of parameters (VP) method is superior to undetermined coefficients (UC) method in that it can applied to cases where UC method fails?
Q2: Please have a look on the attachment. You can see the formula for solving linear nonhomogeneous diff. eq. there. Can I apply that formula to the 2nd order equations with getting the same results as with methods UC and VP?
Q3: Is there an easy way to extend the formula in the attachment to apply to higher order equations (4th order is the highest I'm interested in)?
Please help me with the queries above. Thank you very much for all the help.
Regards
PG
Linear nonhomogeneous differential equations are solved using the following two techniques in the book: (1) Undetermined Coefficients (superposition and annihilator approaches), (2) Variation of Parameters.
The book says undetermined coefficients approaches do not apply when the forcing function (e.g. g(x) in this equation ay'' + by' + cy = g(x)) is: In(x), 1/x, tan(x), arcsin(x) and so on. And in such cases variation of parameters technique is used.
Q1: Does this mean variation of parameters (VP) method is superior to undetermined coefficients (UC) method in that it can applied to cases where UC method fails?
Q2: Please have a look on the attachment. You can see the formula for solving linear nonhomogeneous diff. eq. there. Can I apply that formula to the 2nd order equations with getting the same results as with methods UC and VP?
Q3: Is there an easy way to extend the formula in the attachment to apply to higher order equations (4th order is the highest I'm interested in)?
Please help me with the queries above. Thank you very much for all the help.
Regards
PG
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