# Differences

This shows you the differences between two versions of the page.

hw4 [2012/10/12 12:56] ethanminot |
hw4 [2012/10/12 12:58] (current) ethanminot |
||
---|---|---|---|

Line 15: | Line 15: | ||

**c)** y’’ + 6y’ + 9y = 0 | **c)** y’’ + 6y’ + 9y = 0 | ||

- | **4.** Use the Frobenius Method to solve the following ODEs: | + | **4.** **a)** In class we found a two Bessel functions by applying the Frobenius method to the Bessel equation. Calculate the first and second derivatives of these Bessel functions and confirm that they satisfy the appropriate Bessel equation. |

+ | | ||

+ | **b)** Do the same thing for a Legendre polynomial (chose a Legendre polynomial that is more interesting that y = 1!) | ||

+ | | ||

+ | **5.** Use the Frobenius Method to solve the following ODEs: | ||

**a)** zy’’ - 2y’ + 9(z^5)y = 0 | **a)** zy’’ - 2y’ + 9(z^5)y = 0 | ||

Line 21: | Line 25: | ||

**b)** z²y’’ - (3/2)zy’ + (1 + z)y = 0 | **b)** z²y’’ - (3/2)zy’ + (1 + z)y = 0 | ||

- | **5.** **a)** In class we found a two Bessel functions by applying the Frobenius method to the Bessel equation. Calculate the first and second derivatives of these Bessel functions and confirm that they satisfy the appropriate Bessel equation. | ||

- | |||

- | **b)** Do the same thing for a Legendre polynomial (chose a Legendre polynomial that is more interesting that y = 1!) |