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hw4 [2012/10/12 12:56]
ethanminot
hw4 [2012/10/12 12:58] (current)
ethanminot
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**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.
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+**b)** Do the same thing for a Legendre polynomial (chose a Legendre polynomial that is more interesting that y = 1!)
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+**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
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**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.
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-**b)** Do the same thing for a Legendre polynomial (chose a Legendre polynomial that is more interesting that y = 1!)

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