Higher-Order ODE

Question 1

This is valid for more general ODEs

Answer 1

method of variation of parameter

Question 2

If r(x) is a sum of functions in the first column of the table, choose for yP the sum of the functions in the corresponding lines of the second column.

Answer 2

Sum Rule

Question 3

One solution must be known

Answer 3

reduction of order

Question 4

Second solution can be obtained by solving a first-order ODE

Answer 4

reduction of order

Question 5

If a term in your choice for yp happens to be a solution of the homogeneous ODE corresponding to the given ODE, multiply your choice of yp by x (or x2 if this solution corresponds to a double root of the characteristic equation of the homogeneous ODE.

Answer 5

modification rule

Question 6

This addresses the limitation of the method of undetermined coefficients

Answer 6

method of variation of parameter

Question 7

If r(X) is one of the functions in the first column in the Table, choose yp in the same line and determine its undetermined coefficients by substituting yp and its derivatives into the ODE

Answer 7

basic rule

Question 8

Rules for the Method of Undetermined Coefficients

Answer 8

Basic Rules
Modification Rules
Sum Rules

Question 9

This method is suitable for linear ODEs with
constant coefficients a and b

Answer 9

method of undetermined coefficients