Changes

===Second-Order Equations===

===Second-Order Equations===

 

==Infinite Series==

===Infinite Series===

Keeping in mind how many functions can be represented with infinite sums created with Taylor series, we stop narrow-mindedly assuming a function is some combination of functions we're familiar with, and instead just assume it has an infinite series representation.

Keeping in mind how many functions can be represented with infinite sums created with Taylor series, we stop narrow-mindedly assuming a function is some combination of functions we're familiar with, and instead just assume it has an infinite series representation.

so that for <math>n\geq 2</math>, the coefficient of <math>x^n</math> on the right hand side is  <math>(n+1)(n+2)a_{n+2}-na_n+a_{n-2}</math>.  So we need only set this equal to <math>1/(n!)</math> to find an infinite series representation of our solution.

so that for <math>n\geq 2</math>, the coefficient of <math>x^n</math> on the right hand side is  <math>(n+1)(n+2)a_{n+2}-na_n+a_{n-2}</math>.  So we need only set this equal to <math>1/(n!)</math> to find an infinite series representation of our solution.

==Functional Transformations==

===Functional Transformations===

 

{{MVCalc}}

{{MVCalc}}