Well do what the question suggests...

.

Now integrate both sides...

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- Apr 3rd 2011, 04:29 AM #1

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## y''= (2/x)y' - (2/x^2)y - 1/x^2

Hey everyone, I need help with this past exam paper as I haven't been given any solutions to it so I am unsure how to find the solutions to these problems, so if someone could please show me a stepy by step answer

Consider the following initial value problem:

y''= (2/x)y' - (2/x^2)y - 1/x^2, y(1)=0, y'(1)=1

By observing that the first two terms on the right-hand side of the equation form a total derivative of a function, find the analytical solution of the problem.

- Apr 3rd 2011, 04:48 AM #2

- Apr 3rd 2011, 05:03 AM #3
The DE can be written as...

(1)

... so that it is 'Euler's type'. The solution of the 'incomplete' DE is...

(2)

... where and are the solutions of the 'characteristic equation'...

(3)

... i.e. , . A solution of the 'complete DE' is so that the general solution of the 'complete DE' is...

(4)

The value of and can be derived from the 'initial conditions'...

Kind regards

- Apr 3rd 2011, 05:11 AM #4

- Apr 3rd 2011, 11:10 AM #5

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